59:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, numérico y variacional:@0.500422:0.043661:0.926919:0.043661:0.926919:0.024916:0.500422:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Uso de GeoGebra para representar funciones trigonométricas:@0.073089:0.136836:0.556684:0.136836:0.556684:0.119889:0.073089:0.119889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Vamos a graficar paso a paso la función 2cos(3 ) 1.:@0.073089:0.157052:0.551547:0.157052:0.551547:0.141340:0.073089:0.141340:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.390999:0.157052:0.398473:0.157052:0.398473:0.141617:0.390999:0.141617:0.000000 5:@0.402357:0.156498:0.417690:0.156498:0.417690:0.142782:0.402357:0.142782:0.000000 x:@0.468770:0.157052:0.476225:0.157052:0.476225:0.141617:0.468770:0.141617:0.000000 2 p 2:@0.480109:0.156498:0.535570:0.156498:0.535570:0.142782:0.480109:0.142782:0.000000:0.000000:0.000000:0.000000:0.000000 a. Vamos a graficar la función cos( ), y sobre este mismo gráfico, la función con amplitud 2, 2cos( ).:@0.103210:0.184415:0.889192:0.184415:0.889192:0.168703:0.103210:0.168703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.331286:0.184415:0.338760:0.184415:0.338760:0.168980:0.331286:0.168980:0.000000 5:@0.342643:0.183861:0.357977:0.183861:0.357977:0.170145:0.342643:0.170145:0.000000 x:@0.391257:0.184415:0.398712:0.184415:0.398712:0.168980:0.391257:0.168980:0.000000 y:@0.804923:0.184415:0.812397:0.184415:0.812397:0.168980:0.804923:0.168980:0.000000 5:@0.816281:0.183861:0.831614:0.183861:0.831614:0.170145:0.816281:0.170145:0.000000 x:@0.873803:0.184415:0.881258:0.184415:0.881258:0.168980:0.873803:0.168980:0.000000 b. :@0.381279:0.580607:0.398342:0.580607:0.398342:0.564894:0.381279:0.564894:0.000000:0.000000:0.000000 Graficamos:@0.404996:0.580607:0.494620:0.580607:0.494620:0.563660:0.404996:0.563660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función 2:@0.494620:0.580607:0.612077:0.580607:0.612077:0.564894:0.494620:0.564894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.575981:0.580607:0.583454:0.580607:0.583454:0.565172:0.575981:0.565172:0.000000 5:@0.587761:0.580052:0.603094:0.580052:0.603094:0.566337:0.587761:0.566337:0.000000 Cos:@0.612087:0.580450:0.636264:0.580450:0.636264:0.565716:0.612087:0.565716:0.000000:0.000000:0.000000 (3 ), con amplitud 2, perío-:@0.636264:0.580607:0.870036:0.580607:0.870036:0.564894:0.636264:0.564894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.650125:0.580607:0.657580:0.580607:0.657580:0.565172:0.650125:0.565172:0.000000 1 p:@0.661887:0.580052:0.693805:0.580052:0.693805:0.566337:0.661887:0.566337:0.000000:0.000000:0.000000 do 2 /3 y desfase :@0.404996:0.597249:0.540510:0.597249:0.540510:0.581536:0.404996:0.581536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.437816:0.596694:0.450093:0.596694:0.450093:0.582979:0.437816:0.582979:0.000000 2p:@0.540510:0.596694:0.568121:0.596694:0.568121:0.582979:0.540510:0.582979:0.000000:0.000000 /3.:@0.568121:0.597249:0.586767:0.597249:0.586767:0.581536:0.568121:0.581536:0.000000:0.000000:0.000000 Gráfica de la función coseno :@0.126522:0.682624:0.328636:0.682624:0.328636:0.667626:0.126522:0.667626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con amplitud 2 y período :@0.126522:0.698509:0.307901:0.698509:0.307901:0.683511:0.126522:0.683511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 /3.:@0.126522:0.714395:0.164615:0.714395:0.164615:0.699396:0.126522:0.699396:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.135096:0.713865:0.146816:0.713865:0.146816:0.700773:0.135096:0.700773:0.000000 En :@0.126522:0.218437:0.147976:0.218437:0.147976:0.203438:0.126522:0.203438:0.000000:0.000000:0.000000 Entrada:@0.147975:0.218437:0.201126:0.218437:0.201126:0.203703:0.147975:0.203703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.201126:0.218437:0.204974:0.218437:0.204974:0.203438:0.201126:0.203438:0.000000 escribe:@0.204974:0.218437:0.259355:0.218437:0.259355:0.202260:0.204974:0.202260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.259355:0.218437:0.292669:0.218437:0.292669:0.203438:0.259355:0.203438:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.263203:0.218437:0.270336:0.218437:0.270336:0.203703:0.263203:0.203703:0.000000 5:@0.274184:0.217907:0.288821:0.217907:0.288821:0.204815:0.274184:0.204815:0.000000 Cos:@0.292669:0.218437:0.316844:0.218437:0.316844:0.203703:0.292669:0.203703:0.000000:0.000000:0.000000 . :@0.316846:0.218437:0.323751:0.218437:0.323751:0.203438:0.316846:0.203438:0.000000:0.000000 Enseguida aparece el recuadro :@0.126521:0.234322:0.345011:0.234322:0.345011:0.219324:0.126521:0.219324:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con la función. :@0.126521:0.250207:0.233052:0.250207:0.233052:0.235209:0.126521:0.235209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Selecciónala:@0.233052:0.250207:0.327370:0.250207:0.327370:0.234031:0.233052:0.234031:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 .:@0.327370:0.250207:0.330428:0.250207:0.330428:0.235209:0.327370:0.235209:0.000000 Aparece el gráfico de la :@0.126522:0.511076:0.293882:0.511076:0.293882:0.496077:0.126522:0.496077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función coseno.:@0.126522:0.526961:0.237761:0.526961:0.237761:0.511963:0.126522:0.511963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Da:@0.386622:0.511076:0.407548:0.511076:0.407548:0.494899:0.386622:0.494899:0.000000:0.000000 clic en :@0.407547:0.511076:0.460101:0.511076:0.460101:0.496077:0.407547:0.496077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Vista Gráfica:@0.460101:0.511076:0.543507:0.511076:0.543507:0.496342:0.460101:0.496342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , luego :@0.543507:0.511076:0.594743:0.511076:0.594743:0.496077:0.543507:0.496077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en :@0.386621:0.526961:0.408408:0.526961:0.408408:0.511963:0.386621:0.511963:0.000000:0.000000:0.000000 Eje X:@0.408408:0.526961:0.438858:0.526961:0.438858:0.512227:0.408408:0.512227:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.438858:0.526961:0.454285:0.526961:0.454285:0.511963:0.438858:0.511963:0.000000:0.000000:0.000000 cambia:@0.454285:0.526961:0.509703:0.526961:0.509703:0.510785:0.454285:0.510785:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la distancia :@0.509703:0.526961:0.595043:0.526961:0.595043:0.511963:0.509703:0.511963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en el eje horizontal a /2.:@0.386621:0.542847:0.564927:0.542847:0.564927:0.527848:0.386621:0.527848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.535408:0.542317:0.547128:0.542317:0.547128:0.529225:0.535408:0.529225:0.000000 Ingresa:@0.646721:0.511076:0.702930:0.511076:0.702930:0.494899:0.646721:0.494899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función 2:@0.702929:0.511076:0.817840:0.511076:0.817840:0.496077:0.702929:0.496077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.779800:0.511076:0.786934:0.511076:0.786934:0.496342:0.779800:0.496342:0.000000 5:@0.790781:0.510546:0.805418:0.510546:0.805418:0.497454:0.790781:0.497454:0.000000 Cos x:@0.817840:0.511076:0.853790:0.511076:0.853790:0.496342:0.817840:0.496342:0.000000:0.000000:0.000000:0.000000:0.000000 ( ). :@0.842017:0.511076:0.865351:0.511076:0.865351:0.496077:0.842017:0.496077:0.000000:0.000000:0.000000:0.000000:0.000000 Puedes ver el cambio con la :@0.646720:0.526961:0.845795:0.526961:0.845795:0.511963:0.646720:0.511963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 función original.:@0.646720:0.542847:0.759592:0.542847:0.759592:0.527848:0.646720:0.527848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Gráfica de la función coseno :@0.126522:0.782689:0.328636:0.782689:0.328636:0.767691:0.126522:0.767691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 con amplitud 2, período 2 /3 :@0.126522:0.798575:0.338263:0.798575:0.338263:0.783576:0.126522:0.783576:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.307954:0.798045:0.319673:0.798045:0.319673:0.784953:0.307954:0.784953:0.000000 y desfase :@0.126522:0.814460:0.194239:0.814460:0.194239:0.799462:0.126522:0.799462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2p:@0.194239:0.813931:0.220595:0.813931:0.220595:0.800838:0.194239:0.800838:0.000000:0.000000 /3.:@0.220595:0.814460:0.238394:0.814460:0.238394:0.799462:0.220595:0.799462:0.000000:0.000000:0.000000 Practica la representación gráfica de estas funciones trigonométricas en GeoGebra:@0.132474:0.909053:0.844401:0.909053:0.844401:0.890565:0.132474:0.890565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a.:@0.132474:0.928953:0.145157:0.928953:0.145157:0.912283:0.132474:0.912283:0.000000:0.000000 3:@0.145157:0.928953:0.188928:0.928953:0.188928:0.913240:0.145157:0.913240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.149076:0.928953:0.156550:0.928953:0.156550:0.913518:0.149076:0.913518:0.000000 5:@0.160581:0.928398:0.175914:0.928398:0.175914:0.914683:0.160581:0.914683:0.000000 Sen x:@0.188928:0.928953:0.226828:0.928953:0.226828:0.913518:0.188928:0.913518:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) 1,5. :@0.214496:0.928953:0.319176:0.928953:0.319176:0.913240:0.214496:0.913240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1 p 1:@0.230860:0.928398:0.286744:0.928398:0.286744:0.914683:0.230860:0.914683:0.000000:0.000000:0.000000:0.000000:0.000000 b.:@0.393523:0.928953:0.407365:0.928953:0.407365:0.912283:0.393523:0.912283:0.000000:0.000000 :@0.407365:0.928953:0.446296:0.928953:0.446296:0.913240:0.407365:0.913240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.415427:0.928953:0.422901:0.928953:0.422901:0.913518:0.415427:0.913518:0.000000 5 2:@0.426932:0.928398:0.461630:0.928398:0.461630:0.914683:0.426932:0.914683:0.000000:0.000000:0.000000 Cos x:@0.461630:0.928953:0.508274:0.928953:0.508274:0.913518:0.461630:0.913518:0.000000:0.000000:0.000000:0.000000:0.000000 (2 ) 2. :@0.486958:0.928953:0.552762:0.928953:0.552762:0.913240:0.486958:0.913240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.517183:0.928398:0.532516:0.928398:0.532516:0.914683:0.517183:0.914683:0.000000 c):@0.632817:0.928953:0.646291:0.928953:0.646291:0.912283:0.632817:0.912283:0.000000:0.000000 :@0.646291:0.928953:0.650322:0.928953:0.650322:0.913240:0.646291:0.913240:0.000000 y:@0.674652:0.928953:0.682125:0.928953:0.682125:0.913518:0.674652:0.913518:0.000000 0,5 :@0.682125:0.928953:0.746054:0.928953:0.746054:0.913240:0.682125:0.913240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 2:@0.686156:0.928398:0.720854:0.928398:0.720854:0.914683:0.686156:0.914683:0.000000:0.000000:0.000000 Tan x:@0.746054:0.928953:0.783899:0.928953:0.783899:0.913518:0.746054:0.913518:0.000000:0.000000:0.000000:0.000000:0.000000 ( /2).:@0.771566:0.928953:0.843097:0.928953:0.843097:0.913240:0.771566:0.913240:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 p:@0.787930:0.928398:0.819572:0.928398:0.819572:0.914683:0.787930:0.914683:0.000000:0.000000:0.000000 Competencia digital:@0.142998:0.096946:0.426798:0.096946:0.426798:0.068829:0.142998:0.068829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@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