51:@0.943272:0.974518:0.962770:0.974518:0.962770:0.957377:0.943272:0.957377:0.000000:0.000000 Pensamiento espacial, numérico y variacional:@0.525225:0.043660:0.930049:0.043660:0.930049:0.024915:0.525225:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las características de la :@0.744288:0.179533:0.900211:0.179533:0.900211:0.165248:0.744288:0.165248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función tangente son::@0.744288:0.194662:0.889481:0.194662:0.889481:0.180377:0.744288:0.180377:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Dominio::@0.744288:0.209790:0.824117:0.209790:0.824117:0.195506:0.744288:0.195506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.744288:0.238459:0.747953:0.238459:0.747953:0.224174:0.744288:0.224174:0.000000 p:@0.879053:0.222211:0.891330:0.222211:0.891330:0.208496:0.879053:0.208496:0.000000 2:@0.879807:0.237134:0.888790:0.237134:0.888790:0.221421:0.879807:0.221421:0.000000 h:@0.871122:0.238170:0.877252:0.238170:0.877252:0.204734:0.871122:0.204734:0.000000 h:@0.987424:0.238170:0.981295:0.238170:0.981295:0.204734:0.987424:0.204734:0.000000 Dom:@0.764534:0.231241:0.800134:0.231241:0.800134:0.215806:0.764534:0.215806:0.000000:0.000000:0.000000 (Tan):@0.800134:0.231241:0.836691:0.231241:0.836691:0.215528:0.800134:0.215528:0.000000:0.000000:0.000000:0.000000:0.000000 5 \ :@0.836689:0.230686:0.875031:0.230686:0.875031:0.216970:0.836689:0.216970:0.000000:0.000000:0.000000:0.000000 R:@0.852022:0.230381:0.865312:0.230381:0.865312:0.217484:0.852022:0.217484:0.000000 :@0.875031:0.231241:0.879063:0.231241:0.879063:0.215528:0.875031:0.215528:0.000000 1 p|:@0.893862:0.229646:0.934156:0.229646:0.934156:0.215930:0.893862:0.215930:0.000000:0.000000:0.000000:0.000000 k k :@0.909195:0.230201:0.945034:0.230201:0.945034:0.214765:0.909195:0.214765:0.000000:0.000000:0.000000:0.000000 [:@0.945034:0.230062:0.960368:0.230062:0.960368:0.216014:0.945034:0.216014:0.000000 Z:@0.960368:0.229341:0.977247:0.229341:0.977247:0.216443:0.960368:0.216443:0.000000:0.000000 :@0.744288:0.253588:0.747953:0.253588:0.747953:0.239303:0.744288:0.239303:0.000000 R:@0.763263:0.252806:0.775344:0.252806:0.775344:0.241081:0.763263:0.241081:0.000000 1:@0.775261:0.254117:0.778976:0.254117:0.778976:0.238068:0.775261:0.238068:0.000000 2:@0.778892:0.253588:0.787058:0.253588:0.787058:0.239303:0.778892:0.239303:0.000000 k:@0.786991:0.253588:0.793869:0.253588:0.793869:0.239555:0.786991:0.239555:0.000000 1 p:@0.793802:0.253083:0.831269:0.253083:0.831269:0.240614:0.793802:0.240614:0.000000:0.000000:0.000000 1) /2, en los :@0.807658:0.253588:0.904679:0.253588:0.904679:0.239303:0.807658:0.239303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.851500:0.253588:0.858378:0.253588:0.858378:0.239555:0.851500:0.239555:0.000000 enteros :@0.763246:0.268716:0.816665:0.268716:0.816665:0.254432:0.763246:0.254432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. Recorrido::@0.744288:0.283845:0.830195:0.283845:0.830195:0.269561:0.744288:0.269561:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.744288:0.298974:0.751551:0.298974:0.751551:0.284690:0.744288:0.284690:0.000000:0.000000 Rec:@0.763263:0.298974:0.785301:0.298974:0.785301:0.284942:0.763263:0.284942:0.000000:0.000000:0.000000 (Tan) .:@0.785251:0.298974:0.854077:0.298974:0.854077:0.284690:0.785251:0.284690:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.821714:0.298470:0.835653:0.298470:0.835653:0.286001:0.821714:0.286001:0.000000 R:@0.839167:0.298193:0.851249:0.298193:0.851249:0.286468:0.839167:0.286468:0.000000 3. El período es .:@0.744288:0.314103:0.865732:0.314103:0.865732:0.299819:0.744288:0.299819:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.851743:0.313599:0.862904:0.313599:0.862904:0.301130:0.851743:0.301130:0.000000 4. La función tangente es :@0.744288:0.329232:0.918153:0.329232:0.918153:0.314948:0.744288:0.314948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 impar.:@0.763263:0.344361:0.804055:0.344361:0.804055:0.330077:0.763263:0.330077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5. El período de la :@0.744288:0.359490:0.869434:0.359490:0.869434:0.345206:0.744288:0.345206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función tangente :@0.763263:0.374619:0.885186:0.374619:0.885186:0.360335:0.763263:0.360335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.763263:0.389748:0.770057:0.389748:0.770057:0.375716:0.763263:0.375716:0.000000 :@0.769990:0.389748:0.791108:0.389748:0.791108:0.375464:0.769990:0.375464:0.000000:0.000000:0.000000 5:@0.773587:0.389244:0.787527:0.389244:0.787527:0.376775:0.773587:0.376775:0.000000 Tan Bx:@0.791041:0.389748:0.833160:0.389748:0.833160:0.375716:0.791041:0.375716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) es la :@0.814050:0.389748:0.873639:0.389748:0.873639:0.375464:0.814050:0.375464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 distancia entre dos :@0.763279:0.404877:0.891573:0.404877:0.891573:0.390593:0.763279:0.390593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 asíntotas verticales.:@0.763279:0.420006:0.890164:0.420006:0.890164:0.405722:0.763279:0.405722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.744288:0.439936:0.747953:0.439936:0.747953:0.425651:0.744288:0.425651:0.000000 T:@0.763263:0.439936:0.770642:0.439936:0.770642:0.425904:0.763263:0.425904:0.000000 :@0.770575:0.439936:0.791693:0.439936:0.791693:0.425651:0.770575:0.425651:0.000000:0.000000:0.000000 5:@0.774173:0.439431:0.788112:0.439431:0.788112:0.426963:0.774173:0.426963:0.000000 p:@0.795013:0.432427:0.807291:0.432427:0.807291:0.418711:0.795013:0.418711:0.000000 | |:@0.791627:0.446933:0.810696:0.446933:0.810696:0.433217:0.791627:0.433217:0.000000:0.000000:0.000000 B:@0.796744:0.447488:0.805579:0.447488:0.805579:0.432052:0.796744:0.432052:0.000000 .:@0.811349:0.439936:0.814261:0.439936:0.814261:0.425651:0.811349:0.425651:0.000000 Las características de la :@0.744296:0.462213:0.900218:0.462213:0.900218:0.447929:0.744296:0.447929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función cotangente son::@0.744296:0.477342:0.905721:0.477342:0.905721:0.463058:0.744296:0.463058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Dominio::@0.744288:0.492471:0.824117:0.492471:0.824117:0.478187:0.744288:0.478187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.744288:0.507600:0.747953:0.507600:0.747953:0.493316:0.744288:0.493316:0.000000 Dom:@0.763263:0.507600:0.795499:0.507600:0.795499:0.493568:0.763263:0.493568:0.000000:0.000000:0.000000 (Cot) :@0.795442:0.507600:0.831048:0.507600:0.831048:0.493316:0.795442:0.493316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.830968:0.507096:0.844907:0.507096:0.844907:0.494627:0.830968:0.494627:0.000000 :@0.744288:0.522729:0.747953:0.522729:0.747953:0.508445:0.744288:0.508445:0.000000 h:@0.763042:0.525771:0.769171:0.525771:0.769171:0.507749:0.763042:0.507749:0.000000 h:@0.841713:0.525664:0.835583:0.525664:0.835583:0.507642:0.841713:0.507642:0.000000 k k :@0.767578:0.525610:0.803417:0.525610:0.803417:0.510174:0.767578:0.510174:0.000000:0.000000:0.000000:0.000000 p|:@0.775144:0.525055:0.792539:0.525055:0.792539:0.511339:0.775144:0.511339:0.000000:0.000000 [:@0.803417:0.525471:0.818750:0.525471:0.818750:0.511422:0.803417:0.511422:0.000000 Z:@0.818750:0.524750:0.835630:0.524750:0.835630:0.511852:0.818750:0.511852:0.000000:0.000000 2. Recorrido::@0.744288:0.537858:0.830195:0.537858:0.830195:0.523574:0.744288:0.523574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.744288:0.552987:0.751551:0.552987:0.751551:0.538702:0.744288:0.538702:0.000000:0.000000 Rec:@0.763263:0.552987:0.785301:0.552987:0.785301:0.538955:0.763263:0.538955:0.000000:0.000000:0.000000 (Cot) .:@0.785251:0.552987:0.853140:0.552987:0.853140:0.538702:0.785251:0.538702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.820777:0.552482:0.834716:0.552482:0.834716:0.540014:0.820777:0.540014:0.000000 R:@0.838230:0.552205:0.850312:0.552205:0.850312:0.540480:0.838230:0.540480:0.000000 3. El período es .:@0.744288:0.568116:0.865732:0.568116:0.865732:0.553831:0.744288:0.553831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.851743:0.567611:0.862904:0.567611:0.862904:0.555143:0.851743:0.555143:0.000000 4. La función cotangente :@0.744288:0.583245:0.916563:0.583245:0.916563:0.568960:0.744288:0.568960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es impar.:@0.763263:0.598374:0.821875:0.598374:0.821875:0.584089:0.763263:0.584089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.740287:0.140786:0.838978:0.140786:0.838978:0.125380:0.740287:0.125380:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740287:0.155915:0.828901:0.155915:0.828901:0.140509:0.740287:0.140509:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 4 (Ev. 5) Modela fenómenos periódicos a través de funciones trigonométricas.:@0.084383:0.971366:0.518122:0.971366:0.518122:0.959939:0.084383:0.959939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3.2 Función cotangente:@0.073089:0.136836:0.258073:0.136836:0.258073:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 La función cotangente se denota con :@0.073089:0.164198:0.348999:0.164198:0.348999:0.148486:0.073089:0.148486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cot:@0.348682:0.164198:0.370613:0.164198:0.370613:0.148763:0.348682:0.148763:0.000000:0.000000:0.000000 y se define como sigue: :@0.370550:0.164198:0.552874:0.164198:0.552874:0.148486:0.370550:0.148486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cot( ):@0.288235:0.197246:0.329136:0.197246:0.329136:0.181533:0.288235:0.181533:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.316803:0.197246:0.324258:0.197246:0.324258:0.181811:0.316803:0.181811:0.000000 cos( ):@0.349476:0.190477:0.391555:0.190477:0.391555:0.174764:0.349476:0.174764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.379222:0.190477:0.386677:0.190477:0.386677:0.175042:0.379222:0.175042:0.000000 sen( ):@0.351133:0.204429:0.394003:0.204429:0.394003:0.188716:0.351133:0.188716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.381670:0.204429:0.389125:0.204429:0.389125:0.188993:0.381670:0.188993:0.000000 5:@0.329092:0.197023:0.344426:0.197023:0.344426:0.183307:0.329092:0.183307:0.000000 ; sen( ) 0.:@0.394836:0.197578:0.491419:0.197578:0.491419:0.181865:0.394836:0.181865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.443984:0.197578:0.451439:0.197578:0.451439:0.182142:0.443984:0.182142:0.000000 ?:@0.460109:0.198119:0.475442:0.198119:0.475442:0.182947:0.460109:0.182947:0.000000 Para determinar el dominio de la función cotangente, resolvemos la ecuación siguiente: :@0.073078:0.226729:0.710871:0.226729:0.710871:0.211016:0.073078:0.211016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.073078:0.243370:0.080533:0.243370:0.080533:0.227935:0.073078:0.227935:0.000000 , tal que sen( ) 0. La solución de esta ecuación es :@0.080459:0.243370:0.521865:0.243370:0.521865:0.227658:0.080459:0.227658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.084417:0.243232:0.099750:0.243232:0.099750:0.229183:0.084417:0.229183:0.000000 R:@0.103615:0.242511:0.116905:0.242511:0.116905:0.229613:0.103615:0.229613:0.000000 x:@0.208150:0.243370:0.215605:0.243370:0.215605:0.227935:0.208150:0.227935:0.000000 5:@0.224275:0.242816:0.239608:0.242816:0.239608:0.229100:0.224275:0.229100:0.000000 x:@0.491254:0.243370:0.498709:0.243370:0.498709:0.227935:0.491254:0.227935:0.000000 5 p:@0.502592:0.242816:0.541561:0.242816:0.541561:0.229100:0.502592:0.229100:0.000000:0.000000:0.000000 k:@0.521791:0.243370:0.529357:0.243370:0.529357:0.227935:0.521791:0.227935:0.000000 , . Por lo tanto, :@0.541469:0.243370:0.701332:0.243370:0.701332:0.227658:0.541469:0.227658:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.560391:0.243370:0.567957:0.243370:0.567957:0.227935:0.560391:0.227935:0.000000 [:@0.571841:0.243232:0.587174:0.243232:0.587174:0.229183:0.571841:0.229183:0.000000 Z:@0.591039:0.242511:0.603317:0.242511:0.603317:0.229613:0.591039:0.229613:0.000000 { | sen( ) 0} {:@0.264881:0.272521:0.432387:0.272521:0.432387:0.256809:0.264881:0.256809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.269686:0.272521:0.277140:0.272521:0.277140:0.257086:0.269686:0.257086:0.000000 [:@0.281024:0.272383:0.296358:0.272383:0.296358:0.258334:0.281024:0.258334:0.000000 R:@0.300223:0.271662:0.313513:0.271662:0.313513:0.258764:0.300223:0.258764:0.000000 x:@0.355353:0.272521:0.362808:0.272521:0.362808:0.257086:0.355353:0.257086:0.000000 5:@0.371478:0.271967:0.386811:0.271967:0.386811:0.258251:0.371478:0.258251:0.000000 5 p:@0.408311:0.271967:0.452065:0.271967:0.452065:0.258251:0.408311:0.258251:0.000000:0.000000:0.000000 k:@0.432295:0.272521:0.439861:0.272521:0.439861:0.257086:0.432295:0.257086:0.000000 | },:@0.451973:0.272521:0.514539:0.272521:0.514539:0.256809:0.451973:0.256809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.463698:0.272521:0.471263:0.272521:0.471263:0.257086:0.463698:0.257086:0.000000 [:@0.475147:0.272383:0.490481:0.272383:0.490481:0.258334:0.475147:0.258334:0.000000 Z:@0.494346:0.271662:0.506624:0.271662:0.506624:0.258764:0.494346:0.258764:0.000000 de donde :@0.073078:0.301672:0.148106:0.301672:0.148106:0.285960:0.073078:0.285960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Dom:@0.147958:0.301672:0.183418:0.301672:0.183418:0.286237:0.147958:0.286237:0.000000:0.000000:0.000000 (Cot) \ {:@0.183355:0.301672:0.273956:0.301672:0.273956:0.285960:0.183355:0.285960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.222434:0.301118:0.237767:0.301118:0.237767:0.287402:0.222434:0.287402:0.000000 R:@0.241633:0.300812:0.254923:0.300812:0.254923:0.287915:0.241633:0.287915:0.000000 k:@0.273846:0.301672:0.281411:0.301672:0.281411:0.286237:0.273846:0.286237:0.000000 p:@0.281337:0.301118:0.293615:0.301118:0.293615:0.287402:0.281337:0.287402:0.000000 | }.:@0.293523:0.301672:0.356089:0.301672:0.356089:0.285960:0.293523:0.285960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.305248:0.301672:0.312814:0.301672:0.312814:0.286237:0.305248:0.286237:0.000000 [:@0.316698:0.301534:0.332031:0.301534:0.332031:0.287485:0.316698:0.287485:0.000000 Z:@0.335896:0.300812:0.348174:0.300812:0.348174:0.287915:0.335896:0.287915:0.000000 Determinemos el recorrido de la función cotangente.:@0.073078:0.330823:0.459369:0.330823:0.459369:0.315111:0.073078:0.315111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Obviamente, por definición, :@0.073078:0.359974:0.279125:0.359974:0.279125:0.344262:0.073078:0.344262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Rec:@0.278871:0.359974:0.303113:0.359974:0.303113:0.344539:0.278871:0.344539:0.000000:0.000000:0.000000 (Cot) {cot( ) | sen( ) 0} .:@0.303058:0.359974:0.536977:0.359974:0.536977:0.344262:0.303058:0.344262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.342136:0.359419:0.357470:0.359419:0.357470:0.345704:0.342136:0.345704:0.000000 x:@0.394303:0.359974:0.401758:0.359974:0.401758:0.344539:0.394303:0.344539:0.000000 x:@0.448420:0.359974:0.455875:0.359974:0.455875:0.344539:0.448420:0.344539:0.000000 ?:@0.464545:0.360515:0.479878:0.360515:0.479878:0.345343:0.464545:0.345343:0.000000 ,:@0.501378:0.359836:0.516711:0.359836:0.516711:0.345787:0.501378:0.345787:0.000000 R:@0.520576:0.359114:0.533866:0.359114:0.533866:0.346217:0.520576:0.346217:0.000000 Mostremos que :@0.073059:0.389125:0.191534:0.389125:0.191534:0.373413:0.073059:0.373413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Rec:@0.191381:0.389125:0.215623:0.389125:0.215623:0.373690:0.191381:0.373690:0.000000:0.000000:0.000000 (Cot) , es decir que :@0.215568:0.389125:0.422484:0.389125:0.422484:0.373413:0.215568:0.373413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.254647:0.388570:0.269980:0.388570:0.269980:0.374855:0.254647:0.374855:0.000000 R:@0.273846:0.388265:0.287136:0.388265:0.287136:0.375368:0.273846:0.375368:0.000000 R:@0.386056:0.388265:0.399346:0.388265:0.399346:0.375368:0.386056:0.375368:0.000000 ,:@0.403212:0.388986:0.418545:0.388986:0.418545:0.374938:0.403212:0.374938:0.000000 Rec:@0.422410:0.389125:0.446653:0.389125:0.446653:0.373690:0.422410:0.373690:0.000000:0.000000:0.000000 (Cot).:@0.446598:0.389125:0.484944:0.389125:0.484944:0.373413:0.446598:0.373413:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea , consideramos la ecuación { \ :@0.073078:0.418276:0.408734:0.418276:0.408734:0.402563:0.073078:0.402563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.102695:0.418276:0.110168:0.418276:0.110168:0.402841:0.102695:0.402841:0.000000 [:@0.114052:0.418137:0.129385:0.418137:0.129385:0.404089:0.114052:0.404089:0.000000 R:@0.133251:0.417416:0.146541:0.417416:0.146541:0.404519:0.133251:0.404519:0.000000 x:@0.350677:0.418276:0.358132:0.418276:0.358132:0.402841:0.350677:0.402841:0.000000 [:@0.362016:0.418137:0.377350:0.418137:0.377350:0.404089:0.362016:0.404089:0.000000 R:@0.381215:0.417416:0.394505:0.417416:0.394505:0.404519:0.381215:0.404519:0.000000 k:@0.408642:0.418276:0.416207:0.418276:0.416207:0.402841:0.408642:0.402841:0.000000 p:@0.416134:0.417721:0.428411:0.417721:0.428411:0.404006:0.416134:0.404006:0.000000 | }, tal que cot( ) .:@0.428319:0.418276:0.622958:0.418276:0.622958:0.402563:0.428319:0.402563:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.440045:0.418276:0.447610:0.418276:0.447610:0.402841:0.440045:0.402841:0.000000 [:@0.451494:0.418137:0.466827:0.418137:0.466827:0.404089:0.451494:0.404089:0.000000 Z:@0.470693:0.417416:0.482970:0.417416:0.482970:0.404519:0.470693:0.404519:0.000000 x:@0.577031:0.418276:0.584486:0.418276:0.584486:0.402841:0.577031:0.402841:0.000000 5:@0.593156:0.417721:0.608489:0.417721:0.608489:0.404006:0.593156:0.404006:0.000000 y:@0.612355:0.418276:0.619828:0.418276:0.619828:0.402841:0.612355:0.402841:0.000000 Tenemos :@0.073078:0.452198:0.173894:0.452198:0.173894:0.436485:0.073078:0.436485:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.143264:0.452198:0.150738:0.452198:0.150738:0.436762:0.143264:0.436762:0.000000 5:@0.154622:0.451643:0.169955:0.451643:0.169955:0.437927:0.154622:0.437927:0.000000 cos( ):@0.173898:0.445789:0.215976:0.445789:0.215976:0.430077:0.173898:0.430077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.203644:0.445789:0.211099:0.445789:0.211099:0.430354:0.203644:0.430354:0.000000 sen( ):@0.173898:0.460157:0.216768:0.460157:0.216768:0.444444:0.173898:0.444444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.204435:0.460157:0.211890:0.460157:0.211890:0.444722:0.204435:0.444722:0.000000 , donde :@0.217566:0.452196:0.297378:0.452196:0.297378:0.436484:0.217566:0.436484:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.280758:0.452196:0.288232:0.452196:0.288232:0.436761:0.280758:0.436761:0.000000 2:@0.288158:0.446133:0.293395:0.446133:0.293395:0.436972:0.288158:0.436972:0.000000 5:@0.297305:0.451642:0.312638:0.451642:0.312638:0.437926:0.297305:0.437926:0.000000 cos( ):@0.313880:0.445245:0.361223:0.445245:0.361223:0.429532:0.313880:0.429532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.348890:0.445245:0.356345:0.445245:0.356345:0.429809:0.348890:0.429809:0.000000 sen( ):@0.313880:0.459612:0.362015:0.459612:0.362015:0.443899:0.313880:0.443899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.349682:0.459612:0.357137:0.459612:0.357137:0.444177:0.349682:0.444177:0.000000 .:@0.361598:0.452196:0.364801:0.452196:0.364801:0.436484:0.361598:0.436484:0.000000 De la relación sen ( ) cos ( ) 1 se sigue que: :@0.073089:0.481346:0.427165:0.481346:0.427165:0.465633:0.073089:0.465633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.200725:0.475282:0.205962:0.475282:0.205962:0.466122:0.200725:0.466122:0.000000 x:@0.210720:0.481346:0.218175:0.481346:0.218175:0.465911:0.210720:0.465911:0.000000 1:@0.226845:0.480791:0.242178:0.480791:0.242178:0.467076:0.226845:0.467076:0.000000 2:@0.270666:0.475282:0.275903:0.475282:0.275903:0.466122:0.270666:0.466122:0.000000 x:@0.280661:0.481346:0.288116:0.481346:0.288116:0.465911:0.280661:0.465911:0.000000 5:@0.296786:0.480791:0.312119:0.480791:0.312119:0.467076:0.296786:0.467076:0.000000 y:@0.073083:0.510497:0.080556:0.510497:0.080556:0.495062:0.073083:0.495062:0.000000 2:@0.080496:0.504433:0.085733:0.504433:0.085733:0.495273:0.080496:0.495273:0.000000 sen ( ) cos ( ) :@0.085686:0.510497:0.207275:0.510497:0.207275:0.494784:0.085686:0.494784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.111104:0.504433:0.116341:0.504433:0.116341:0.495273:0.111104:0.495273:0.000000 y:@0.121098:0.510497:0.128571:0.510497:0.128571:0.495062:0.121098:0.495062:0.000000 5:@0.137241:0.509942:0.152574:0.509942:0.152574:0.496227:0.137241:0.496227:0.000000 2:@0.181065:0.504433:0.186301:0.504433:0.186301:0.495273:0.181065:0.495273:0.000000 x:@0.191058:0.510497:0.198513:0.510497:0.198513:0.495062:0.191058:0.495062:0.000000 ⇔:@0.207183:0.510081:0.226363:0.510081:0.226363:0.493093:0.207183:0.493093:0.000000 sen ( ) 1 sen ( ) :@0.226271:0.510497:0.397231:0.510497:0.397231:0.494784:0.226271:0.494784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.230229:0.510497:0.237702:0.510497:0.237702:0.495062:0.230229:0.495062:0.000000 2:@0.237633:0.504433:0.242870:0.504433:0.242870:0.495273:0.237633:0.495273:0.000000 2:@0.268241:0.504433:0.273478:0.504433:0.273478:0.495273:0.268241:0.495273:0.000000 x:@0.278237:0.510497:0.285691:0.510497:0.285691:0.495062:0.278237:0.495062:0.000000 5 2:@0.294361:0.509942:0.341742:0.509942:0.341742:0.496227:0.294361:0.496227:0.000000:0.000000:0.000000 2:@0.371019:0.504433:0.376256:0.504433:0.376256:0.495273:0.371019:0.495273:0.000000 x:@0.381014:0.510497:0.388469:0.510497:0.388469:0.495062:0.381014:0.495062:0.000000 ⇔:@0.397139:0.510081:0.416319:0.510081:0.416319:0.493093:0.397139:0.493093:0.000000 sen ( ) sen ( ) 1 :@0.416227:0.510497:0.587263:0.510497:0.587263:0.494784:0.416227:0.494784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.420185:0.510497:0.427658:0.510497:0.427658:0.495062:0.420185:0.495062:0.000000 2:@0.427590:0.504433:0.432826:0.504433:0.432826:0.495273:0.427590:0.495273:0.000000 2:@0.458198:0.504433:0.463434:0.504433:0.463434:0.495273:0.458198:0.495273:0.000000 x:@0.468191:0.510497:0.475646:0.510497:0.475646:0.495062:0.468191:0.495062:0.000000 1:@0.484316:0.509942:0.499649:0.509942:0.499649:0.496227:0.484316:0.496227:0.000000 2:@0.528930:0.504433:0.534167:0.504433:0.534167:0.495273:0.528930:0.495273:0.000000 x:@0.538925:0.510497:0.546380:0.510497:0.546380:0.495062:0.538925:0.495062:0.000000 5:@0.555050:0.509942:0.570383:0.509942:0.570383:0.496227:0.555050:0.496227:0.000000 ⇔:@0.237359:0.543295:0.256539:0.543295:0.256539:0.526307:0.237359:0.526307:0.000000 ( 1)sen ( ) 1 :@0.256447:0.543711:0.398319:0.543711:0.398319:0.527999:0.256447:0.527999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.265191:0.543711:0.272664:0.543711:0.272664:0.528276:0.265191:0.528276:0.000000 2:@0.272611:0.537648:0.277847:0.537648:0.277847:0.528487:0.272611:0.528487:0.000000 1:@0.281759:0.543157:0.297092:0.543157:0.297092:0.529441:0.281759:0.529441:0.000000 2:@0.340061:0.537648:0.345298:0.537648:0.345298:0.528487:0.340061:0.528487:0.000000 x:@0.350055:0.543711:0.357510:0.543711:0.357510:0.528276:0.350055:0.528276:0.000000 5:@0.366180:0.543157:0.381513:0.543157:0.381513:0.529441:0.366180:0.529441:0.000000 ⇔:@0.398227:0.543295:0.417407:0.543295:0.417407:0.526307:0.398227:0.526307:0.000000 sen ( ) :@0.417315:0.543711:0.492077:0.543711:0.492077:0.527999:0.417315:0.527999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.446686:0.537648:0.451923:0.537648:0.451923:0.528487:0.446686:0.528487:0.000000 x:@0.456680:0.543711:0.464135:0.543711:0.464135:0.528276:0.456680:0.528276:0.000000 5:@0.472805:0.543157:0.488138:0.543157:0.488138:0.529441:0.472805:0.529441:0.000000 1:@0.510369:0.536775:0.519351:0.536775:0.519351:0.520341:0.510369:0.520341:0.000000 y :@0.494189:0.550796:0.510240:0.550796:0.510240:0.535360:0.494189:0.535360:0.000000:0.000000:0.000000 :@0.501662:0.550796:0.506927:0.550796:0.506927:0.534362:0.501662:0.534362:0.000000 1 :@0.510240:0.550241:0.530175:0.550241:0.530175:0.536525:0.510240:0.536525:0.000000:0.000000 1:@0.530175:0.550796:0.539158:0.550796:0.539158:0.534362:0.530175:0.534362:0.000000 .:@0.538858:0.543711:0.542061:0.543711:0.542061:0.527999:0.538858:0.527999:0.000000 Como 0 sen ( ) 1, :@0.073081:0.575137:0.258613:0.575132:0.258613:0.559419:0.073081:0.559424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.136253:0.574582:0.151586:0.574582:0.151586:0.560866:0.136253:0.560866:0.000000 2:@0.181854:0.569068:0.187091:0.569068:0.187091:0.559907:0.181854:0.559907:0.000000 x:@0.191997:0.575132:0.199452:0.575132:0.199452:0.559696:0.191997:0.559696:0.000000 #:@0.208895:0.574577:0.224228:0.574577:0.224228:0.560861:0.208895:0.560861:0.000000 ;:@0.259128:0.574577:0.271406:0.574577:0.271406:0.560861:0.259128:0.560861:0.000000 x:@0.271424:0.575132:0.278879:0.575132:0.278879:0.559696:0.271424:0.559696:0.000000 , 0 :@0.278898:0.575132:0.357276:0.575132:0.357276:0.559419:0.278898:0.559419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.283426:0.574993:0.298759:0.574993:0.298759:0.560945:0.283426:0.560945:0.000000 R:@0.303306:0.574272:0.316596:0.574272:0.316596:0.561374:0.303306:0.561374:0.000000 #:@0.337893:0.574577:0.353226:0.574577:0.353226:0.560861:0.337893:0.560861:0.000000 1:@0.376146:0.569990:0.385129:0.569990:0.385129:0.553557:0.376146:0.553557:0.000000 y :@0.359966:0.584011:0.376018:0.584011:0.376018:0.568576:0.359966:0.568576:0.000000:0.000000:0.000000 :@0.367440:0.584011:0.372704:0.584011:0.372704:0.567577:0.367440:0.567577:0.000000 1 :@0.376018:0.583456:0.395953:0.583456:0.395953:0.569741:0.376018:0.569741:0.000000:0.000000 1:@0.395951:0.584011:0.404934:0.584011:0.404934:0.567577:0.395951:0.567577:0.000000 1, :@0.404733:0.575132:0.458979:0.575132:0.458979:0.559419:0.404733:0.559419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.409261:0.574577:0.424594:0.574577:0.424594:0.560861:0.409261:0.560861:0.000000 ;:@0.459494:0.574577:0.471772:0.574577:0.471772:0.560861:0.459494:0.560861:0.000000 y:@0.471790:0.575132:0.479264:0.575132:0.479264:0.559696:0.471790:0.559696:0.000000 , se sigue que la ecuación :@0.479282:0.575132:0.710385:0.575132:0.710385:0.559419:0.479282:0.559419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.483810:0.574993:0.499144:0.574993:0.499144:0.560945:0.483810:0.560945:0.000000 R:@0.503690:0.574272:0.516980:0.574272:0.516980:0.561374:0.503690:0.561374:0.000000 sen ( ) :@0.073089:0.597099:0.143898:0.597105:0.143898:0.581393:0.073089:0.581386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.098507:0.591041:0.103744:0.591041:0.103744:0.581881:0.098507:0.581881:0.000000 x:@0.108501:0.597105:0.115956:0.597105:0.115956:0.581670:0.108501:0.581670:0.000000 5:@0.124626:0.596551:0.139959:0.596551:0.139959:0.582835:0.124626:0.582835:0.000000 1:@0.162190:0.588902:0.171173:0.588902:0.171173:0.572468:0.162190:0.572468:0.000000 y :@0.146011:0.602922:0.162062:0.602922:0.162062:0.587487:0.146011:0.587487:0.000000:0.000000:0.000000 :@0.153484:0.602922:0.158748:0.602922:0.158748:0.586488:0.153484:0.586488:0.000000 1 :@0.162062:0.602368:0.181997:0.602368:0.181997:0.588652:0.162062:0.588652:0.000000:0.000000 1:@0.181995:0.602922:0.190978:0.602922:0.190978:0.586488:0.181995:0.586488:0.000000 tiene solución en \ {:@0.190680:0.597105:0.355701:0.597105:0.355701:0.581393:0.190680:0.581393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 R:@0.323378:0.596245:0.336668:0.596245:0.336668:0.583348:0.323378:0.583348:0.000000 k:@0.355590:0.597105:0.363156:0.597105:0.363156:0.581670:0.355590:0.581670:0.000000 p:@0.363082:0.596551:0.375360:0.596551:0.375360:0.582835:0.363082:0.582835:0.000000 | }.:@0.375268:0.597105:0.434778:0.597105:0.434778:0.581393:0.375268:0.581393:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.386993:0.597105:0.394559:0.597105:0.394559:0.581670:0.386993:0.581670:0.000000 p:@0.398443:0.596551:0.410720:0.596551:0.410720:0.582835:0.398443:0.582835:0.000000 Z:@0.414586:0.596245:0.426863:0.596245:0.426863:0.583348:0.414586:0.583348:0.000000 De todos estos resultados, la función cotangente está definida como sigue: :@0.073094:0.626256:0.620154:0.626256:0.620154:0.610544:0.073094:0.610544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Cot: :@0.298289:0.666640:0.331083:0.666640:0.331083:0.650928:0.298289:0.650928:0.000000:0.000000:0.000000:0.000000:0.000000 cos( ).:@0.434297:0.666871:0.481148:0.666638:0.481148:0.650925:0.434297:0.651158:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.464043:0.666871:0.471498:0.666871:0.471498:0.651436:0.464043:0.651436:0.000000 sen( ):@0.435051:0.681237:0.477922:0.681237:0.477922:0.665525:0.435051:0.665525:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.465589:0.681237:0.473044:0.681237:0.473044:0.665802:0.465589:0.665802:0.000000 R :@0.339775:0.652142:0.357667:0.652142:0.357667:0.639244:0.339775:0.639244:0.000000:0.000000 \ p:@0.357667:0.652447:0.387229:0.652447:0.387229:0.638731:0.357667:0.638731:0.000000:0.000000:0.000000:0.000000 k:@0.367386:0.653002:0.374952:0.653002:0.374952:0.637566:0.367386:0.637566:0.000000 ) :@0.387229:0.653002:0.396138:0.653002:0.396138:0.637289:0.387229:0.637289:0.000000:0.000000 → :@0.396138:0.653681:0.418908:0.653681:0.418908:0.638066:0.396138:0.638066:0.000000:0.000000 R:@0.418908:0.652142:0.432198:0.652142:0.432198:0.639244:0.418908:0.639244:0.000000 x :@0.339223:0.674220:0.349991:0.674220:0.349991:0.658785:0.339223:0.658785:0.000000:0.000000 →:@0.349991:0.674899:0.368159:0.674899:0.368159:0.659284:0.349991:0.659284:0.000000 cot( ) :@0.368159:0.674220:0.413091:0.674220:0.413091:0.658507:0.368159:0.658507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.396727:0.674220:0.404182:0.674220:0.404182:0.658785:0.396727:0.658785:0.000000 5 :@0.413091:0.673665:0.433026:0.673665:0.433026:0.659950:0.413091:0.659950:0.000000:0.000000 h:@0.331937:0.684484:0.338067:0.684484:0.338067:0.629441:0.331937:0.629441:0.000000 Verifiquemos que es periódica de período .:@0.073089:0.695788:0.395879:0.695788:0.395879:0.680075:0.073089:0.680075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.380490:0.695233:0.392768:0.695233:0.392768:0.681517:0.380490:0.681517:0.000000 Tenemos cos( ) cos( ), sen( ) sen( ), :@0.073089:0.724938:0.480846:0.724938:0.480846:0.709226:0.073089:0.709226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.172691:0.724938:0.180146:0.724938:0.180146:0.709503:0.172691:0.709503:0.000000 1 p 5 2:@0.184030:0.724384:0.258689:0.724384:0.258689:0.710668:0.184030:0.710668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.288012:0.724938:0.295467:0.724938:0.295467:0.709503:0.288012:0.709503:0.000000 x:@0.337472:0.724938:0.344927:0.724938:0.344927:0.709503:0.337472:0.709503:0.000000 1 p 5 2:@0.348811:0.724384:0.423471:0.724384:0.423471:0.710668:0.348811:0.710668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.453585:0.724938:0.461040:0.724938:0.461040:0.709503:0.453585:0.709503:0.000000 ;:@0.480736:0.724384:0.493014:0.724384:0.493014:0.710668:0.480736:0.710668:0.000000 x:@0.492922:0.724938:0.500377:0.724938:0.500377:0.709503:0.492922:0.709503:0.000000 . Luego,:@0.500303:0.724938:0.592674:0.724938:0.592674:0.709226:0.500303:0.709226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.504261:0.724800:0.519594:0.724800:0.519594:0.710751:0.504261:0.710751:0.000000 R:@0.523459:0.724079:0.536749:0.724079:0.536749:0.711181:0.523459:0.711181:0.000000 cot( ) :@0.073071:0.758680:0.172046:0.758680:0.172046:0.742967:0.073071:0.742967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.101307:0.758680:0.108762:0.758680:0.108762:0.743244:0.101307:0.743244:0.000000 1 p 5:@0.112646:0.758125:0.168107:0.758125:0.168107:0.744409:0.112646:0.744409:0.000000:0.000000:0.000000:0.000000:0.000000 cos(:@0.172525:0.751768:0.202271:0.751768:0.202271:0.736056:0.172525:0.736056:0.000000:0.000000:0.000000:0.000000 x :@0.202271:0.751768:0.213040:0.751768:0.213040:0.736333:0.202271:0.736333:0.000000:0.000000 1 p:@0.213040:0.751214:0.245252:0.751214:0.245252:0.737498:0.213040:0.737498:0.000000:0.000000:0.000000 ):@0.245251:0.751768:0.250129:0.751768:0.250129:0.736056:0.245251:0.736056:0.000000 sen(:@0.173334:0.766136:0.203871:0.766136:0.203871:0.750423:0.173334:0.750423:0.000000:0.000000:0.000000:0.000000 x :@0.203871:0.766136:0.214639:0.766136:0.214639:0.750701:0.203871:0.750701:0.000000:0.000000 1 p:@0.214639:0.765581:0.246852:0.765581:0.246852:0.751865:0.214639:0.751865:0.000000:0.000000:0.000000 ):@0.246852:0.766136:0.251730:0.766136:0.251730:0.750423:0.246852:0.750423:0.000000 2:@0.276233:0.751214:0.291567:0.751214:0.291567:0.737498:0.276233:0.737498:0.000000 cos( ):@0.291567:0.751768:0.333646:0.751768:0.333646:0.736056:0.291567:0.736056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.321313:0.751768:0.328768:0.751768:0.328768:0.736333:0.321313:0.736333:0.000000 2:@0.276675:0.765581:0.292008:0.765581:0.292008:0.751865:0.276675:0.751865:0.000000 sen( ):@0.292008:0.766136:0.334879:0.766136:0.334879:0.750423:0.292008:0.750423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.322546:0.766136:0.330001:0.766136:0.330001:0.750701:0.322546:0.750701:0.000000 5:@0.255848:0.758314:0.271182:0.758314:0.271182:0.744599:0.255848:0.744599:0.000000 cos( ):@0.356795:0.751768:0.398874:0.751768:0.398874:0.736056:0.356795:0.736056:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.386541:0.751768:0.393996:0.751768:0.393996:0.736333:0.386541:0.736333:0.000000 sen( ):@0.357605:0.766136:0.400476:0.766136:0.400476:0.750423:0.357605:0.750423:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.388143:0.766136:0.395598:0.766136:0.395598:0.750701:0.388143:0.750701:0.000000 5:@0.337854:0.758314:0.353188:0.758314:0.353188:0.744599:0.337854:0.744599:0.000000 cot( ), :@0.400924:0.758675:0.471737:0.758675:0.471737:0.742962:0.400924:0.742962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.404882:0.758120:0.420215:0.758120:0.420215:0.744404:0.404882:0.744404:0.000000 x:@0.452317:0.758675:0.459772:0.758675:0.459772:0.743239:0.452317:0.743239:0.000000 x:@0.073091:0.787826:0.080546:0.787826:0.080546:0.772390:0.073091:0.772390:0.000000 \ {:@0.080472:0.787826:0.135952:0.787826:0.135952:0.772113:0.080472:0.772113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.084430:0.787687:0.099763:0.787687:0.099763:0.773639:0.084430:0.773639:0.000000 R:@0.103629:0.786966:0.116919:0.786966:0.116919:0.774068:0.103629:0.774068:0.000000 k:@0.135841:0.787826:0.143407:0.787826:0.143407:0.772390:0.135841:0.772390:0.000000 p:@0.143333:0.787271:0.155611:0.787271:0.155611:0.773555:0.143333:0.773555:0.000000 | }.:@0.155519:0.787826:0.218085:0.787826:0.218085:0.772113:0.155519:0.772113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.167244:0.787826:0.174810:0.787826:0.174810:0.772390:0.167244:0.772390:0.000000 [:@0.178693:0.787687:0.194027:0.787687:0.194027:0.773639:0.178693:0.773639:0.000000 Z:@0.197892:0.786966:0.210170:0.786966:0.210170:0.774068:0.197892:0.774068:0.000000 La función cotangente es impar. En efecto, :@0.073091:0.816977:0.384787:0.816977:0.384787:0.801264:0.073091:0.801264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cot(:@0.073091:0.851966:0.105396:0.851966:0.105396:0.836253:0.073091:0.836253:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.105285:0.851411:0.151985:0.851411:0.151985:0.837696:0.105285:0.837696:0.000000:0.000000:0.000000 x:@0.120527:0.851966:0.127981:0.851966:0.127981:0.836531:0.120527:0.836531:0.000000 ) :@0.127908:0.851966:0.155924:0.851966:0.155924:0.836253:0.127908:0.836253:0.000000:0.000000:0.000000:0.000000 cos(:@0.156680:0.844465:0.186426:0.844465:0.186426:0.828752:0.156680:0.828752:0.000000:0.000000:0.000000:0.000000 2:@0.186426:0.843910:0.201759:0.843910:0.201759:0.830194:0.186426:0.830194:0.000000 x:@0.201759:0.844465:0.209214:0.844465:0.209214:0.829029:0.201759:0.829029:0.000000 ):@0.209214:0.844465:0.214092:0.844465:0.214092:0.828752:0.209214:0.828752:0.000000 sen(:@0.157490:0.858832:0.188028:0.858832:0.188028:0.843119:0.157490:0.843119:0.000000:0.000000:0.000000:0.000000 2:@0.188028:0.858277:0.203361:0.858277:0.203361:0.844562:0.188028:0.844562:0.000000 x:@0.203361:0.858832:0.210816:0.858832:0.210816:0.843397:0.203361:0.843397:0.000000 ):@0.210816:0.858832:0.215694:0.858832:0.215694:0.843119:0.210816:0.843119:0.000000 cos( ):@0.246387:0.844465:0.288466:0.844465:0.288466:0.828752:0.246387:0.828752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.276133:0.844465:0.283588:0.844465:0.283588:0.829029:0.276133:0.829029:0.000000 2:@0.238453:0.858277:0.253787:0.858277:0.253787:0.844562:0.238453:0.844562:0.000000 cos( ):@0.253787:0.858832:0.295866:0.858832:0.295866:0.843119:0.253787:0.843119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.283533:0.858832:0.290988:0.858832:0.290988:0.843397:0.283533:0.843397:0.000000 5:@0.218806:0.851012:0.234139:0.851012:0.234139:0.837296:0.218806:0.837296:0.000000 cos( ):@0.336256:0.844465:0.378335:0.844465:0.378335:0.828752:0.336256:0.828752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.366002:0.844465:0.373457:0.844465:0.373457:0.829029:0.366002:0.829029:0.000000 sen( ):@0.337066:0.858832:0.379937:0.858832:0.379937:0.843119:0.337066:0.843119:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.367604:0.858832:0.375059:0.858832:0.375059:0.843397:0.367604:0.843397:0.000000 52:@0.300812:0.851012:0.331479:0.851012:0.331479:0.837296:0.300812:0.837296:0.000000:0.000000 cot( ), \ {:@0.379654:0.851967:0.528403:0.851967:0.528403:0.836255:0.379654:0.836255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.383611:0.851413:0.418143:0.851413:0.418143:0.837697:0.383611:0.837697:0.000000:0.000000:0.000000 x x:@0.446288:0.851967:0.472997:0.851967:0.472997:0.836532:0.446288:0.836532:0.000000:0.000000:0.000000 [:@0.476881:0.851829:0.492214:0.851829:0.492214:0.837780:0.476881:0.837780:0.000000 R:@0.496080:0.851108:0.509370:0.851108:0.509370:0.838210:0.496080:0.838210:0.000000 k:@0.528292:0.851967:0.535858:0.851967:0.535858:0.836532:0.528292:0.836532:0.000000 p:@0.535784:0.851413:0.548062:0.851413:0.548062:0.837697:0.535784:0.837697:0.000000 | }.:@0.547970:0.851967:0.610536:0.851967:0.610536:0.836255:0.547970:0.836255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.559695:0.851967:0.567261:0.851967:0.567261:0.836532:0.559695:0.836532:0.000000 [:@0.571144:0.851829:0.586478:0.851829:0.586478:0.837780:0.571144:0.837780:0.000000 Z:@0.590343:0.851108:0.602621:0.851108:0.602621:0.838210:0.590343:0.838210:0.000000 En la Figura 5.11., se muestra el gráfico de la función cotangente y su grafo se define :@0.073081:0.881118:0.684478:0.881118:0.684478:0.865406:0.073081:0.865406:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como sigue::@0.073081:0.897760:0.161878:0.897760:0.161878:0.882047:0.073081:0.882047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G(Cot) {( , cot( )) | \{:@0.222658:0.926911:0.469826:0.926909:0.469826:0.911197:0.222658:0.911198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.273131:0.926356:0.288464:0.926356:0.288464:0.912641:0.273131:0.912641:0.000000 x:@0.301920:0.926911:0.309375:0.926911:0.309375:0.911476:0.301920:0.911476:0.000000 x:@0.344625:0.926911:0.352080:0.926911:0.352080:0.911476:0.344625:0.911476:0.000000 [:@0.365554:0.926772:0.380887:0.926772:0.380887:0.912724:0.365554:0.912724:0.000000 R:@0.384753:0.926051:0.398043:0.926051:0.398043:0.913154:0.384753:0.913154:0.000000 2:@0.397966:0.920845:0.403203:0.920845:0.403203:0.911685:0.397966:0.911685:0.000000 x:@0.414880:0.926909:0.422335:0.926909:0.422335:0.911474:0.414880:0.911474:0.000000 [:@0.426219:0.926771:0.441552:0.926771:0.441552:0.912722:0.426219:0.912722:0.000000 R:@0.445418:0.926049:0.458708:0.926049:0.458708:0.913152:0.445418:0.913152:0.000000 k:@0.469734:0.926909:0.477299:0.926909:0.477299:0.911474:0.469734:0.911474:0.000000 p:@0.477226:0.926354:0.489503:0.926354:0.489503:0.912639:0.477226:0.912639:0.000000 | }}.:@0.489411:0.926909:0.556782:0.926909:0.556782:0.911197:0.489411:0.911197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.501137:0.926909:0.508702:0.926909:0.508702:0.911474:0.501137:0.911474:0.000000 [:@0.512586:0.926771:0.527919:0.926771:0.527919:0.912722:0.512586:0.912722:0.000000 Z:@0.531785:0.926049:0.544062:0.926049:0.544062:0.913152:0.531785:0.913152:0.000000 Figura 5.11.:@0.866725:0.940006:0.926913:0.940006:0.926913:0.928578:0.866725:0.928578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.918123:0.862710:0.922867:0.862710:0.922867:0.852888:0.918123:0.852888:0.000000 y:@0.780184:0.786383:0.784940:0.786383:0.784940:0.776561:0.780184:0.776561:0.000000 y:@0.793844:0.806310:0.798141:0.806310:0.798141:0.797434:0.793844:0.797434:0.000000 cot( ):@0.798141:0.806310:0.833418:0.806310:0.833418:0.797275:0.798141:0.797275:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.799612:0.805991:0.808429:0.805991:0.808429:0.798104:0.799612:0.798104:0.000000 x:@0.826327:0.806310:0.830613:0.806310:0.830613:0.797434:0.826327:0.797434:0.000000 p:@0.826589:0.858707:0.832365:0.858707:0.832365:0.852254:0.826589:0.852254:0.000000 0:@0.791076:0.857779:0.795159:0.857779:0.795159:0.850637:0.791076:0.850637:0.000000 3:@0.844599:0.859295:0.848825:0.859295:0.848825:0.851902:0.844599:0.851902:0.000000 p:@0.848825:0.859033:0.854601:0.859033:0.854601:0.852581:0.848825:0.852581:0.000000 2:@0.847786:0.865597:0.852012:0.865597:0.852012:0.858205:0.847786:0.858205:0.000000 5:@0.882132:0.859295:0.886358:0.859295:0.886358:0.851902:0.882132:0.851902:0.000000 p:@0.886358:0.859033:0.892134:0.859033:0.892134:0.852581:0.886358:0.852581:0.000000 2:@0.885327:0.865597:0.889553:0.865597:0.889553:0.858205:0.885327:0.858205:0.000000 2:@0.863600:0.859295:0.867826:0.859295:0.867826:0.851902:0.863600:0.851902:0.000000 p:@0.867826:0.859033:0.873602:0.859033:0.873602:0.852581:0.867826:0.852581:0.000000 3:@0.901625:0.859295:0.905851:0.859295:0.905851:0.851902:0.901625:0.851902:0.000000 p:@0.905851:0.859033:0.911627:0.859033:0.911627:0.852581:0.905851:0.852581:0.000000 p:@0.767162:0.859033:0.772938:0.859033:0.772938:0.852581:0.767162:0.852581:0.000000 2:@0.767932:0.865597:0.772158:0.865597:0.772158:0.858205:0.767932:0.858205:0.000000 p:@0.807141:0.859033:0.812917:0.859033:0.812917:0.852581:0.807141:0.852581:0.000000 2:@0.807920:0.865597:0.812146:0.865597:0.812146:0.858205:0.807920:0.858205:0.000000 3:@0.727283:0.859295:0.731509:0.859295:0.731509:0.851902:0.727283:0.851902:0.000000 p:@0.731509:0.859033:0.737285:0.859033:0.737285:0.852581:0.731509:0.852581:0.000000 2:@0.730167:0.865597:0.734393:0.865597:0.734393:0.858205:0.730167:0.858205:0.000000 2p:@0.746083:0.858707:0.759073:0.858707:0.759073:0.852255:0.746083:0.852255:0.000000:0.000000 2 p 2:@0.704335:0.859033:0.726244:0.861532:0.726244:0.855080:0.704335:0.852581:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.711548:0.859295:0.715774:0.859295:0.715774:0.851902:0.711548:0.851902:0.000000 2:@0.759160:0.861532:0.766373:0.861532:0.766373:0.855080:0.759160:0.855080:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000