116:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000
Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.º BG:@0.120102:0.967458:0.162238:0.967458:0.162238:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
isposición y compromiso:@0.306727:0.140863:0.485691:0.140863:0.485691:0.125499:0.306727:0.125499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.284763:0.141649:0.297589:0.141649:0.297589:0.124513:0.284763:0.124513:0.000000
Una identidad trigonométrica es una igualdad que involucra funciones trigonométricas :@0.287495:0.437978:0.907678:0.437978:0.907678:0.421589:0.287495:0.421589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y se cumple para todos los valores del ángulo en los que están definidas.:@0.287495:0.454575:0.818814:0.454575:0.818814:0.438186:0.287495:0.438186:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identidades recíprocas y de cociente:@0.287495:0.483768:0.654630:0.483768:0.654630:0.462258:0.287495:0.462258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Son aquellas que relacionan una función con su inversa multiplicativa. Resultan de las :@0.287495:0.502986:0.907698:0.502986:0.907698:0.486597:0.287495:0.486597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
razones trigonométricas que revisamos en el tema 1.:@0.287495:0.519582:0.673512:0.519582:0.673512:0.503193:0.287495:0.503193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
senx:@0.449672:0.551205:0.486509:0.551205:0.486509:0.534843:0.449672:0.534843:0.000000:0.000000:0.000000:0.000000
cscx:@0.510925:0.562047:0.547173:0.562047:0.547173:0.545686:0.510925:0.545686:0.000000:0.000000:0.000000:0.000000
cosx:@0.449359:0.589833:0.486767:0.589833:0.486767:0.573471:0.449359:0.573471:0.000000:0.000000:0.000000:0.000000
secx:@0.511497:0.600676:0.547744:0.600676:0.547744:0.584314:0.511497:0.584314:0.000000:0.000000:0.000000:0.000000
tanx:@0.448769:0.628461:0.486177:0.628461:0.486177:0.612099:0.448769:0.612099:0.000000:0.000000:0.000000:0.000000
cotx:@0.510594:0.639304:0.547725:0.639304:0.547725:0.622942:0.510594:0.622942:0.000000:0.000000:0.000000:0.000000
():@0.472375:0.551218:0.493180:0.551218:0.493180:0.534829:0.472375:0.534829:0.000000:0.000000
():@0.533067:0.562049:0.553872:0.562049:0.553872:0.545660:0.533067:0.545660:0.000000:0.000000
():@0.472655:0.589826:0.493459:0.589826:0.493459:0.573437:0.472655:0.573437:0.000000:0.000000
():@0.533643:0.600671:0.554448:0.600671:0.554448:0.584282:0.533643:0.584282:0.000000:0.000000
():@0.472078:0.628449:0.492883:0.628449:0.492883:0.612060:0.472078:0.612060:0.000000:0.000000
():@0.533643:0.639294:0.554448:0.639294:0.554448:0.622905:0.533643:0.622905:0.000000:0.000000
=:@0.496160:0.551882:0.506277:0.551882:0.506277:0.536309:0.496160:0.536309:0.000000
=:@0.496418:0.590510:0.506535:0.590510:0.506535:0.574937:0.496418:0.574937:0.000000
=:@0.495847:0.629138:0.505963:0.629138:0.505963:0.613565:0.495847:0.613565:0.000000
1:@0.528514:0.542442:0.537507:0.542442:0.537507:0.526053:0.528514:0.526053:0.000000
1:@0.528933:0.581064:0.537925:0.581064:0.537925:0.564675:0.528933:0.564675:0.000000
1:@0.528675:0.619692:0.537667:0.619692:0.537667:0.603303:0.528675:0.603303:0.000000
tanx:@0.627809:0.551164:0.665217:0.551164:0.665217:0.534803:0.627809:0.534803:0.000000:0.000000:0.000000:0.000000
senx:@0.692357:0.542403:0.729194:0.542403:0.729194:0.526042:0.692357:0.526042:0.000000:0.000000:0.000000:0.000000
cosx:@0.694242:0.562009:0.731650:0.562009:0.731650:0.545647:0.694242:0.545647:0.000000:0.000000:0.000000:0.000000
cotx:@0.628382:0.610539:0.665513:0.610539:0.665513:0.594178:0.628382:0.594178:0.000000:0.000000:0.000000:0.000000
cosx:@0.692565:0.601771:0.729973:0.601771:0.729973:0.585409:0.692565:0.585409:0.000000:0.000000:0.000000:0.000000
senx:@0.690262:0.621382:0.727098:0.621382:0.727098:0.605021:0.690262:0.605021:0.000000:0.000000:0.000000:0.000000
():@0.651103:0.551166:0.671908:0.551166:0.671908:0.534777:0.651103:0.534777:0.000000:0.000000
():@0.715079:0.542403:0.735883:0.542403:0.735883:0.526015:0.715079:0.526015:0.000000:0.000000
():@0.717548:0.562015:0.738353:0.562015:0.738353:0.545626:0.717548:0.545626:0.000000:0.000000
():@0.651419:0.610533:0.672224:0.610533:0.672224:0.594144:0.651419:0.594144:0.000000:0.000000
():@0.715863:0.601771:0.736667:0.601771:0.736667:0.585382:0.715863:0.585382:0.000000:0.000000
() :@0.712988:0.621382:0.738116:0.621381:0.738116:0.604992:0.712988:0.604993:0.000000:0.000000:0.000000
=:@0.674873:0.551842:0.684990:0.551842:0.684990:0.536269:0.674873:0.536269:0.000000
=:@0.675186:0.611216:0.685303:0.611216:0.685303:0.595643:0.675186:0.595643:0.000000
 :@0.690205:0.562007:0.694240:0.562007:0.694240:0.545618:0.690205:0.545618:0.000000
Identidades pitagóricas:@0.287495:0.662310:0.491901:0.662310:0.491901:0.643873:0.287495:0.643873:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En el círculo unitario se cumple   =   +   dividimos para   :@0.287495:0.682156:0.718439:0.682156:0.718439:0.665767:0.287495:0.665767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
r:@0.517435:0.682156:0.522724:0.682156:0.522724:0.665795:0.517435:0.665795:0.000000
2:@0.522763:0.676109:0.528005:0.676109:0.528005:0.666554:0.522763:0.666554:0.000000
x:@0.545955:0.682156:0.553418:0.682156:0.553418:0.665795:0.545955:0.665795:0.000000
2:@0.553431:0.676109:0.558674:0.676109:0.558674:0.666554:0.553431:0.666554:0.000000
y:@0.576623:0.682156:0.584105:0.682156:0.584105:0.665795:0.576623:0.665795:0.000000
2:@0.584118:0.676109:0.589361:0.676109:0.589361:0.666554:0.584118:0.666554:0.000000
r:@0.703853:0.682156:0.709142:0.682156:0.709142:0.665795:0.703853:0.665795:0.000000
2:@0.709162:0.676109:0.714404:0.676109:0.714404:0.666554:0.709162:0.666554:0.000000
y reemplazamos   = :@0.287490:0.698753:0.438394:0.698753:0.438394:0.682364:0.287490:0.682364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.411877:0.698753:0.419340:0.698753:0.419340:0.682391:0.411877:0.682391:0.000000
r.cos θ:@0.438394:0.698753:0.483466:0.698753:0.483466:0.682391:0.438394:0.682391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) y   = :@0.469517:0.698753:0.531065:0.698753:0.531065:0.682364:0.469517:0.682364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.504529:0.698753:0.512011:0.698753:0.512011:0.682391:0.504529:0.682391:0.000000
r.sen θ:@0.531065:0.698753:0.576729:0.698753:0.576729:0.682391:0.531065:0.682391:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ), tenemos:@0.562779:0.698753:0.653959:0.698753:0.653959:0.682364:0.562779:0.682364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos θ:@0.429936:0.722472:0.472221:0.722477:0.472221:0.706115:0.429936:0.706110:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.453029:0.716429:0.458272:0.716429:0.458272:0.706874:0.453029:0.706874:0.000000
( ) + :@0.458271:0.722477:0.496158:0.722477:0.496158:0.706088:0.458271:0.706088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen θ:@0.496158:0.722477:0.539029:0.722477:0.539029:0.706115:0.496158:0.706115:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.519838:0.716429:0.525080:0.716429:0.525080:0.706874:0.519838:0.706874:0.000000
( ) = 1:@0.525080:0.722477:0.571960:0.722477:0.571960:0.706088:0.525080:0.706088:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
También se comprueban las identidades::@0.287492:0.746196:0.587844:0.746196:0.587844:0.729807:0.287492:0.729807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.353649:0.770551:0.362642:0.770551:0.362642:0.754881:0.353649:0.754881:0.000000
1   :@0.506359:0.770551:0.506892:0.770551:0.506892:0.754881:0.506359:0.754881:0.000000:0.000000:0.000000:0.000000
2:@0.398736:0.762878:0.403948:0.762878:0.403948:0.753797:0.398736:0.753797:0.000000
2:@0.465644:0.762878:0.470856:0.762878:0.470856:0.753797:0.465644:0.753797:0.000000
2:@0.551746:0.762878:0.556958:0.762878:0.556958:0.753797:0.551746:0.753797:0.000000
2:@0.618334:0.762878:0.623545:0.762878:0.623545:0.753797:0.618334:0.753797:0.000000
+:@0.362352:0.771228:0.305613:0.771228:0.305613:0.755655:0.362352:0.755655:0.000000
=:@0.429207:0.771228:0.372469:0.771228:0.372469:0.755655:0.429207:0.755655:0.000000
+:@0.515048:0.771228:0.457996:0.771228:0.457996:0.755655:0.515048:0.755655:0.000000
=:@0.582217:0.771228:0.525165:0.771228:0.525165:0.755655:0.582217:0.755655:0.000000
tan θ:@0.374747:0.770551:0.421129:0.770551:0.421129:0.755158:0.374747:0.755158:0.000000:0.000000:0.000000:0.000000:0.000000
sec θ:@0.442800:0.770551:0.488040:0.770551:0.488040:0.755158:0.442800:0.755158:0.000000:0.000000:0.000000:0.000000:0.000000
cot θ:@0.528046:0.770551:0.574171:0.770551:0.574171:0.755158:0.528046:0.755158:0.000000:0.000000:0.000000:0.000000:0.000000
csc θ:@0.595510:0.770551:0.640750:0.770551:0.640750:0.755158:0.595510:0.755158:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.405429:0.770551:0.426234:0.770551:0.426234:0.754881:0.405429:0.754881:0.000000:0.000000
();:@0.472340:0.770551:0.496332:0.770551:0.496332:0.754881:0.472340:0.754881:0.000000:0.000000:0.000000
( ):@0.558470:0.770551:0.579259:0.770551:0.579259:0.754881:0.558470:0.754881:0.000000:0.000000:0.000000
( ):@0.625051:0.770551:0.645836:0.770551:0.645836:0.754881:0.625051:0.754881:0.000000:0.000000:0.000000
Funciones de la suma y diferencia de dos ángulos :@0.287495:0.799936:0.681622:0.799936:0.681622:0.783036:0.287495:0.783036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Para dos ángulos cualesquiera, se cumplen las siguientes identidades trigonométricas.:@0.287495:0.820101:0.902422:0.820101:0.902422:0.803712:0.287495:0.803712:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tanx:@0.616182:0.852942:0.653591:0.852942:0.653591:0.837549:0.616182:0.837549:0.000000:0.000000:0.000000:0.000000
y:@0.672092:0.852942:0.679574:0.852942:0.679574:0.837549:0.672092:0.837549:0.000000
tanx:@0.707362:0.844187:0.744771:0.844187:0.744771:0.828794:0.707362:0.828794:0.000000:0.000000:0.000000:0.000000
tany:@0.766202:0.844187:0.803886:0.844187:0.803886:0.828794:0.766202:0.828794:0.000000:0.000000:0.000000:0.000000
tanx tany:@0.726933:0.863771:0.807848:0.863771:0.807848:0.848378:0.726933:0.848378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tanx y:@0.616146:0.892842:0.679223:0.892842:0.679223:0.877449:0.616146:0.877449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tanx:@0.709961:0.884088:0.747369:0.884088:0.747369:0.868694:0.709961:0.868694:0.000000:0.000000:0.000000:0.000000
tan y:@0.768487:0.884088:0.806213:0.884100:0.806213:0.868707:0.768487:0.868694:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.639438:0.852928:0.644321:0.852928:0.644321:0.837258:0.639438:0.837258:0.000000
):@0.681324:0.852928:0.686208:0.852928:0.686208:0.837258:0.681324:0.837258:0.000000
():@0.730637:0.844173:0.751441:0.844173:0.751441:0.828504:0.730637:0.828504:0.000000:0.000000
():@0.789476:0.844173:0.810539:0.844173:0.810539:0.828504:0.789476:0.828504:0.000000:0.000000
():@0.750207:0.863757:0.771011:0.863757:0.771011:0.848087:0.750207:0.848087:0.000000:0.000000
():@0.793497:0.863777:0.814559:0.863777:0.814559:0.848107:0.793497:0.848107:0.000000:0.000000
(:@0.639478:0.892852:0.644362:0.892852:0.644362:0.877182:0.639478:0.877182:0.000000
):@0.681051:0.892852:0.685934:0.892852:0.685934:0.877182:0.681051:0.877182:0.000000
():@0.733293:0.884098:0.754098:0.884098:0.754098:0.868428:0.733293:0.868428:0.000000:0.000000
( ):@0.791820:0.884098:0.812847:0.884100:0.812847:0.868430:0.791820:0.868428:0.000000:0.000000:0.000000
+:@0.657703:0.853616:0.636309:0.853616:0.636309:0.838043:0.657703:0.838043:0.000000
=:@0.689215:0.853616:0.667820:0.853616:0.667820:0.838043:0.689215:0.838043:0.000000
+:@0.753803:0.844861:0.763920:0.844861:0.763920:0.829288:0.753803:0.829288:0.000000
−:@0.657703:0.893516:0.636622:0.893516:0.636622:0.877943:0.657703:0.877943:0.000000
=:@0.688901:0.893516:0.667820:0.893516:0.667820:0.877943:0.688901:0.877943:0.000000
−:@0.756420:0.884761:0.766537:0.884761:0.766537:0.869189:0.756420:0.869189:0.000000
 1  :@0.703091:0.863767:0.730198:0.863767:0.730198:0.848097:0.703091:0.848097:0.000000:0.000000:0.000000:0.000000
−:@0.716045:0.864445:0.726162:0.864445:0.726162:0.848872:0.716045:0.848872:0.000000
y:@0.798732:0.884100:0.806213:0.884100:0.806213:0.868707:0.798732:0.868707:0.000000
tanx tany:@0.732134:0.903711:0.813050:0.903711:0.813050:0.888318:0.732134:0.888318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.755408:0.903711:0.776213:0.903711:0.776213:0.888042:0.755408:0.888042:0.000000:0.000000
():@0.798680:0.903715:0.819743:0.903715:0.819743:0.888046:0.798680:0.888046:0.000000:0.000000
 1+ :@0.704238:0.903715:0.732230:0.903715:0.732230:0.888046:0.704238:0.888046:0.000000:0.000000:0.000000:0.000000
senx:@0.290583:0.842682:0.327420:0.842682:0.327420:0.826321:0.290583:0.826321:0.000000:0.000000:0.000000:0.000000
y:@0.345921:0.842682:0.353403:0.842682:0.353403:0.826321:0.345921:0.826321:0.000000
sen xcos y:@0.376658:0.842682:0.457574:0.842682:0.457574:0.826321:0.376658:0.826321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos xsen y:@0.479558:0.842682:0.560824:0.842682:0.560824:0.826321:0.479558:0.826321:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
senx y:@0.290583:0.863428:0.353089:0.863428:0.353089:0.847066:0.290583:0.847066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen xcos y:@0.376345:0.863428:0.457261:0.863428:0.457261:0.847066:0.376345:0.847066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cossx seny:@0.478932:0.863428:0.560161:0.863428:0.560161:0.847066:0.478932:0.847066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.313304:0.842682:0.318187:0.842682:0.318187:0.826293:0.313304:0.826293:0.000000
):@0.355190:0.842682:0.360074:0.842682:0.360074:0.826293:0.355190:0.826293:0.000000
():@0.399361:0.842682:0.420166:0.842682:0.420166:0.826293:0.399361:0.826293:0.000000:0.000000
():@0.443182:0.842682:0.464245:0.842682:0.464245:0.826293:0.443182:0.826293:0.000000:0.000000
():@0.502869:0.842682:0.523674:0.842682:0.523674:0.826293:0.502869:0.826293:0.000000:0.000000
():@0.546432:0.842682:0.567495:0.842682:0.567495:0.826293:0.546432:0.826293:0.000000:0.000000
(:@0.313304:0.863428:0.318187:0.863428:0.318187:0.847039:0.313304:0.847039:0.000000
):@0.354877:0.863428:0.359760:0.863428:0.359760:0.847039:0.354877:0.847039:0.000000
():@0.399048:0.863428:0.419853:0.863428:0.419853:0.847039:0.399048:0.847039:0.000000:0.000000
():@0.442869:0.863428:0.463932:0.863428:0.463932:0.847039:0.442869:0.847039:0.000000:0.000000
+:@0.331511:0.843360:0.341627:0.843360:0.341627:0.827787:0.331511:0.827787:0.000000
=:@0.363022:0.843360:0.373139:0.843360:0.373139:0.827787:0.363022:0.827787:0.000000
+:@0.466585:0.843360:0.476702:0.843360:0.476702:0.827787:0.466585:0.827787:0.000000
−:@0.331511:0.864105:0.341627:0.864105:0.341627:0.848532:0.331511:0.848532:0.000000
=:@0.362709:0.864105:0.372825:0.864105:0.372825:0.848532:0.362709:0.848532:0.000000
−:@0.466254:0.864105:0.476370:0.864105:0.476370:0.848532:0.466254:0.848532:0.000000
cosx:@0.290233:0.884173:0.327641:0.884173:0.327641:0.867812:0.290233:0.867812:0.000000:0.000000:0.000000:0.000000
y:@0.346142:0.884173:0.353624:0.884173:0.353624:0.867812:0.346142:0.867812:0.000000
cos xcos y:@0.376566:0.884173:0.458072:0.884173:0.458072:0.867812:0.376566:0.867812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen xsen y:@0.480056:0.884173:0.560732:0.884173:0.560732:0.867812:0.480056:0.867812:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cosx:@0.290233:0.904918:0.327641:0.904918:0.327641:0.888557:0.290233:0.888557:0.000000:0.000000:0.000000:0.000000
y:@0.346142:0.904918:0.353624:0.904918:0.353624:0.888557:0.346142:0.888557:0.000000
cos xxcos y:@0.376566:0.904918:0.458112:0.904918:0.458112:0.888557:0.376566:0.888557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
():@0.502206:0.863428:0.523011:0.863428:0.523011:0.847039:0.502206:0.847039:0.000000:0.000000
():@0.545796:0.863428:0.566858:0.863428:0.566858:0.847039:0.545796:0.847039:0.000000:0.000000
(:@0.313566:0.884173:0.318449:0.884173:0.318449:0.867784:0.313566:0.867784:0.000000
):@0.355452:0.884173:0.360335:0.884173:0.360335:0.867784:0.355452:0.867784:0.000000
():@0.399899:0.884173:0.420704:0.884173:0.420704:0.867784:0.399899:0.867784:0.000000:0.000000
():@0.443720:0.884173:0.464783:0.884173:0.464783:0.867784:0.443720:0.867784:0.000000:0.000000
():@0.502817:0.884173:0.523622:0.884173:0.523622:0.867784:0.502817:0.867784:0.000000:0.000000
():@0.546372:0.884173:0.567435:0.884173:0.567435:0.867784:0.546372:0.867784:0.000000:0.000000
(:@0.313566:0.904918:0.318449:0.904918:0.318449:0.888530:0.313566:0.888530:0.000000
):@0.355452:0.904918:0.360335:0.904918:0.360335:0.888530:0.355452:0.888530:0.000000
( ):@0.399899:0.904918:0.420704:0.904918:0.420704:0.888530:0.399899:0.888530:0.000000:0.000000:0.000000
+:@0.331790:0.884851:0.341907:0.884851:0.341907:0.869278:0.331790:0.869278:0.000000
=:@0.363302:0.884851:0.373418:0.884851:0.373418:0.869278:0.363302:0.869278:0.000000
−:@0.467123:0.884851:0.477240:0.884851:0.477240:0.869278:0.467123:0.869278:0.000000
+:@0.331790:0.905596:0.341907:0.905596:0.341907:0.890023:0.331790:0.890023:0.000000
=:@0.363302:0.905596:0.373418:0.905596:0.373418:0.890023:0.363302:0.890023:0.000000
sen xsen y:@0.480428:0.904918:0.561086:0.904918:0.561086:0.888557:0.480428:0.888557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.443720:0.904918:0.464783:0.904918:0.464783:0.888530:0.443720:0.888530:0.000000:0.000000:0.000000
( ):@0.503149:0.904918:0.523927:0.904918:0.523927:0.888530:0.503149:0.888530:0.000000:0.000000:0.000000
( ):@0.546685:0.904918:0.567746:0.904918:0.567746:0.888530:0.546685:0.888530:0.000000:0.000000:0.000000
+:@0.467113:0.905596:0.477230:0.905596:0.477230:0.890023:0.467113:0.890023:0.000000
nidad de conocimientos:@0.306727:0.410623:0.480398:0.410623:0.480398:0.395259:0.306727:0.395259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
U:@0.284892:0.411408:0.297460:0.411408:0.297460:0.394272:0.284892:0.394272:0.000000
Pienso y progreso:@0.294883:0.359677:0.417347:0.359677:0.417347:0.344313:0.294883:0.344313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Por qué los triángulos son usados en estructuras y edificaciones?:@0.294883:0.378329:0.730843:0.378329:0.730843:0.363430:0.294883:0.363430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una identidad es una igualdad que siempre se cumple, independientemente de los :@0.287495:0.168345:0.907598:0.168345:0.907598:0.151956:0.287495:0.151956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valores que tomen sus variables. Las identidades trigonométricas permiten relacionar :@0.287495:0.184941:0.907731:0.184941:0.907731:0.168553:0.287495:0.168553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre sí las diferentes razones trigonométricas y utilizarlas para modelar fenómenos :@0.287495:0.201538:0.907683:0.201538:0.907683:0.185149:0.287495:0.185149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales, como el movimiento ondulatorio, el análisis de corrientes eléctricas o el cálculo :@0.287495:0.218134:0.907620:0.218134:0.907620:0.201745:0.287495:0.201745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de alturas y distancias inaccesibles, entre otras aplicaciones.:@0.287495:0.234731:0.722620:0.234731:0.722620:0.218342:0.287495:0.218342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rodrigo desea colocar una escalera contra una pared para pintar su casa. Quiere ase-:@0.287495:0.258450:0.903642:0.258450:0.903642:0.242061:0.287495:0.242061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
gurarse de que la escalera esté en un ángulo seguro para evitar accidentes. La escalera :@0.287495:0.275046:0.907585:0.275046:0.907585:0.258657:0.287495:0.258657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mide 5 metros de largo y el pie de esta la ubica a 1,5 metros de la pared.:@0.287495:0.291642:0.814537:0.291642:0.814537:0.275253:0.287495:0.275253:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.287495:0.311807:0.302403:0.311807:0.302403:0.294906:0.287495:0.294906:0.000000:0.000000
  ¿A qué ángulo se encuentra inclinada la escalera ?:@0.302403:0.311807:0.682160:0.311807:0.682160:0.295418:0.302403:0.295418:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.287495:0.335526:0.303712:0.335526:0.303712:0.318625:0.287495:0.318625:0.000000:0.000000
  Si   es el ángulo de inclinación, verifica que se cumple :@0.303712:0.335526:0.716819:0.335526:0.716819:0.319137:0.303712:0.319137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
θ:@0.332422:0.335526:0.341488:0.335526:0.341488:0.319165:0.332422:0.319165:0.000000
sen θ:@0.716819:0.335526:0.759689:0.335532:0.759689:0.319171:0.716819:0.319165:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.740497:0.329485:0.745740:0.329485:0.745740:0.319930:0.740497:0.319930:0.000000
( ) + :@0.745739:0.335532:0.783626:0.335532:0.783626:0.319143:0.745739:0.319143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos θ:@0.783626:0.335532:0.825907:0.335532:0.825907:0.319171:0.783626:0.319171:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.806716:0.329485:0.811959:0.329485:0.811959:0.319930:0.806716:0.319930:0.000000
( ) = 1:@0.811958:0.335532:0.858838:0.335532:0.858838:0.319143:0.811958:0.319143:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuándo una expresión :@0.086944:0.192000:0.247832:0.192000:0.247832:0.177101:0.086944:0.177101:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática es igual a :@0.098905:0.207088:0.247834:0.207088:0.247834:0.192189:0.098905:0.192189:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otra? :@0.211146:0.222175:0.247834:0.222175:0.247834:0.207276:0.211146:0.207276:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.108521:0.163125:0.227756:0.163125:0.227756:0.146224:0.108521:0.146224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Identidades trigonométricas:@0.286308:0.075160:0.706716:0.075160:0.706716:0.041608:0.286308:0.041608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.094760:0.108603:0.159692:0.108603:0.159692:0.011514:0.094760:0.011514:0.000000
y:@0.796450:0.647466:0.799532:0.647466:0.799532:0.641576:0.796450:0.641576:0.000000
x:@0.908175:0.721828:0.911257:0.721828:0.911257:0.715937:0.908175:0.715937:0.000000
r:@0.821642:0.694941:0.823865:0.694941:0.823865:0.689051:0.821642:0.689051:0.000000
(:@0.853608:0.676232:0.855593:0.676232:0.855593:0.670300:0.853608:0.670300:0.000000
x, y:@0.855593:0.676232:0.864503:0.676232:0.864503:0.670342:0.855593:0.670342:0.000000:0.000000:0.000000:0.000000
):@0.864503:0.676232:0.866488:0.676232:0.866488:0.670300:0.864503:0.670300:0.000000
θ:@0.819965:0.713472:0.823606:0.713472:0.823606:0.707566:0.819965:0.707566:0.000000
y:@0.855805:0.703552:0.858887:0.703552:0.858887:0.697661:0.855805:0.697661:0.000000
x:@0.825691:0.721825:0.828774:0.721825:0.828774:0.715935:0.825691:0.715935:0.000000
©Shutterstock:@0.070380:0.372318:0.070380:0.329493:0.058469:0.329493:0.058469:0.372318:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La trigonometría es una :@0.072616:0.426363:0.218847:0.426363:0.218847:0.412954:0.072616:0.412954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
herramienta fundamental; :@0.072616:0.438935:0.233006:0.438935:0.233006:0.425526:0.072616:0.425526:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
permite calcular distancias, :@0.072616:0.451507:0.237436:0.451507:0.237436:0.438098:0.072616:0.438098:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
alturas y ángulos de manera :@0.072616:0.464079:0.244752:0.464079:0.244752:0.450669:0.072616:0.450669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
indirecta.:@0.072616:0.476650:0.127813:0.476650:0.127813:0.463241:0.072616:0.463241:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Lleva un presupuesto. Así :@0.075644:0.600488:0.248425:0.600488:0.248425:0.585589:0.075644:0.585589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
puedes comparar lo que :@0.080988:0.615576:0.248428:0.615576:0.248428:0.600677:0.080988:0.600677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ganas con lo que gastas, :@0.081876:0.630663:0.248425:0.630663:0.248425:0.615764:0.081876:0.615764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ajustar lo que sea :@0.129151:0.645751:0.248428:0.645751:0.248428:0.630852:0.129151:0.630852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
necesario y asegurarte de :@0.074002:0.660839:0.248425:0.660839:0.248425:0.645940:0.074002:0.645940:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no gastar más de lo que :@0.084456:0.675926:0.248428:0.675926:0.248428:0.661027:0.084456:0.661027:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tienes. Un buen :@0.139822:0.691014:0.248428:0.691014:0.248428:0.676115:0.139822:0.676115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
presupuesto te ayuda a :@0.088677:0.706101:0.248426:0.706101:0.248426:0.691202:0.088677:0.691202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tomar decisiones más :@0.099365:0.721189:0.248428:0.721189:0.248428:0.706290:0.099365:0.706290:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
inteligentes y a alcanzar :@0.085863:0.736277:0.248426:0.736277:0.248426:0.721378:0.085863:0.721378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tus metas financieras.:@0.102146:0.751364:0.244758:0.751364:0.244758:0.736465:0.102146:0.736465:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Averigua a tus padres si :@0.096718:0.862999:0.247773:0.862999:0.247773:0.848125:0.096718:0.848125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
realizan un presupuesto :@0.093468:0.878086:0.247771:0.878086:0.247771:0.863213:0.093468:0.863213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
familiar.:@0.192777:0.893174:0.244758:0.893174:0.244758:0.878300:0.192777:0.878300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Educación  :@0.142411:0.560848:0.227718:0.560848:0.227718:0.543947:0.142411:0.543947:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
financiera:@0.145592:0.574678:0.220641:0.574678:0.220641:0.557778:0.145592:0.557778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
©Shutterstock:@0.066818:0.817430:0.066818:0.774605:0.054907:0.774605:0.054907:0.817430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000