79:@0.942772:0.974518:0.963274:0.974518:0.963274:0.956333:0.942772:0.956333:0.000000:0.000000 Pensamiento espacial, métrico, numérico y variacional:@0.418515:0.043661:0.926917:0.043661:0.926917:0.024916:0.418515:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Uso de una calculadora graficadora para solucionar ecuaciones trigonométricas:@0.073089:0.138097:0.753827:0.138097:0.753827:0.119609:0.073089:0.119609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Consideremos la ecuación :@0.073089:0.169447:0.268412:0.169447:0.268412:0.153013:0.073089:0.153013:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cosx:@0.268279:0.169447:0.298648:0.169447:0.298648:0.153041:0.268279:0.153041:0.000000:0.000000:0.000000:0.000000 = :@0.298596:0.169447:0.317574:0.169447:0.317574:0.153013:0.298596:0.153013:0.000000:0.000000:0.000000 senx :@0.317574:0.169447:0.351701:0.169447:0.351701:0.153041:0.317574:0.153041:0.000000:0.000000:0.000000:0.000000:0.000000 + :@0.351738:0.169447:0.366666:0.169447:0.366666:0.153013:0.351738:0.153013:0.000000:0.000000 1:@0.373700:0.161678:0.382683:0.161678:0.382683:0.145244:0.373700:0.145244:0.000000 2 :@0.373700:0.175810:0.386714:0.175810:0.386714:0.159376:0.373700:0.159376:0.000000:0.000000 . La queremos resolver en el intervalo [0,2 π), apoyados en una calculadora :@0.389622:0.169444:0.931372:0.169444:0.931372:0.153010:0.389622:0.153010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 graficadora.:@0.073091:0.186086:0.157960:0.186086:0.157960:0.169652:0.073091:0.169652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Inicialmente, hacemos = ( ) = :@0.073091:0.216859:0.306753:0.216859:0.306753:0.200426:0.073091:0.200426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.240063:0.216859:0.247537:0.216859:0.247537:0.200453:0.240063:0.200453:0.000000 f x:@0.266257:0.216859:0.283136:0.216859:0.283136:0.200453:0.266257:0.200453:0.000000:0.000000:0.000000 cosx:@0.306642:0.216859:0.337011:0.216859:0.337011:0.200453:0.306642:0.200453:0.000000:0.000000:0.000000:0.000000 y = ( ) = :@0.336959:0.216859:0.487346:0.216859:0.487346:0.200426:0.336959:0.200426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.416092:0.216859:0.423565:0.216859:0.423565:0.200453:0.416092:0.200453:0.000000 g x:@0.442285:0.216859:0.463730:0.216859:0.463730:0.200453:0.442285:0.200453:0.000000:0.000000:0.000000 senx:@0.487236:0.216859:0.518123:0.216859:0.518123:0.200453:0.487236:0.200453:0.000000:0.000000:0.000000:0.000000 + :@0.518086:0.216859:0.536972:0.216859:0.536972:0.200426:0.518086:0.200426:0.000000:0.000000:0.000000 1:@0.543920:0.209985:0.552903:0.209985:0.552903:0.193551:0.543920:0.193551:0.000000 2 :@0.543920:0.224116:0.556934:0.224116:0.556934:0.207683:0.543920:0.207683:0.000000:0.000000 :@0.559934:0.216863:0.567997:0.216863:0.567997:0.200429:0.559934:0.200429:0.000000:0.000000 Luego, con ayuda de la calculadora graficadora, hacemos las gráficas de ( ) y ( ).:@0.073099:0.244225:0.670231:0.244225:0.670231:0.227791:0.073099:0.227791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.595424:0.244225:0.612303:0.244225:0.612303:0.227819:0.595424:0.227819:0.000000:0.000000:0.000000 g x:@0.640853:0.244225:0.662297:0.244225:0.662297:0.227819:0.640853:0.227819:0.000000:0.000000:0.000000 Cuando tengamos las dos gráficas, identificamos los puntos (x,y) de corte de las gráficas. Las abscisas de estos puntos :@0.073099:0.271587:0.931269:0.271587:0.931269:0.255153:0.073099:0.255153:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.508652:0.271587:0.517414:0.271587:0.517414:0.255181:0.508652:0.255181:0.000000 finalmente nos darán las soluciones de la ecuación dada inicialmente y en el intervalo que nos indicaron. Debemos :@0.073099:0.288229:0.930204:0.288229:0.930204:0.271795:0.073099:0.271795:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tener en cuenta las ayudas de la calculadora graficadora para lograr ver la gráfica en el intervalo en el que estamos :@0.073099:0.304871:0.931063:0.304871:0.931063:0.288437:0.073099:0.288437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 buscando la solución.:@0.073099:0.321513:0.230242:0.321513:0.230242:0.305079:0.073099:0.305079:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 https://www.desmos.com/calculator:@0.718541:0.637724:0.926765:0.637724:0.926765:0.624301:0.718541:0.624301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ya ubicados en la gráfica, observamos que en el intervalo [0, 2 ) hay dos puntos que tienen coordenadas (0.424, 0.911) :@0.073089:0.665717:0.931178:0.665717:0.931178:0.649284:0.073089:0.649284:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.516888:0.665163:0.529165:0.665163:0.529165:0.651447:0.516888:0.651447:0.000000 y (4.288, -0.411), por tanto, hay dos soluciones que son las abscisas = 0,424 y = 4,288.:@0.073089:0.682359:0.703537:0.682359:0.703537:0.665926:0.073089:0.665926:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x :@0.555948:0.682359:0.566643:0.682359:0.566643:0.665953:0.555948:0.665953:0.000000:0.000000 x :@0.636075:0.682359:0.646769:0.682359:0.646769:0.665953:0.636075:0.665953:0.000000:0.000000 Miremos ahora la solución por un método algebraico para comparar y confirmar las soluciones.:@0.073089:0.709721:0.762562:0.709721:0.762562:0.693287:0.073089:0.693287:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cosx:@0.103203:0.740495:0.133571:0.740495:0.133571:0.724089:0.103203:0.724089:0.000000:0.000000:0.000000:0.000000 = :@0.133520:0.740495:0.152406:0.740495:0.152406:0.724061:0.133520:0.724061:0.000000:0.000000:0.000000 senx:@0.152314:0.740495:0.183201:0.740495:0.183201:0.724089:0.152314:0.724089:0.000000:0.000000:0.000000:0.000000 + :@0.183164:0.740495:0.202050:0.740495:0.202050:0.724061:0.183164:0.724061:0.000000:0.000000:0.000000 1:@0.208970:0.733619:0.217953:0.733619:0.217953:0.717185:0.208970:0.717185:0.000000 2 :@0.208970:0.747750:0.221984:0.747750:0.221984:0.731317:0.208970:0.731317:0.000000:0.000000 :@0.224892:0.740497:0.248711:0.740497:0.248711:0.724064:0.224892:0.724064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cos x:@0.248601:0.740497:0.288069:0.740495:0.288069:0.724089:0.248601:0.724091:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.271468:0.734431:0.276705:0.734431:0.276705:0.724850:0.271468:0.724850:0.000000 = (:@0.276657:0.740495:0.311686:0.740495:0.311686:0.724061:0.276657:0.724061:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 senx:@0.311575:0.740495:0.342463:0.740495:0.342463:0.724089:0.311575:0.724089:0.000000:0.000000:0.000000:0.000000 + :@0.342426:0.740495:0.361312:0.740495:0.361312:0.724061:0.342426:0.724061:0.000000:0.000000:0.000000 1:@0.368245:0.733619:0.377227:0.733619:0.377227:0.717185:0.368245:0.717185:0.000000 2 :@0.368245:0.747750:0.381259:0.747750:0.381259:0.731317:0.368245:0.731317:0.000000:0.000000 ) :@0.384167:0.740497:0.417973:0.740495:0.417973:0.724061:0.384167:0.724064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.392922:0.734431:0.398159:0.734431:0.398159:0.724850:0.392922:0.724850:0.000000 cos x:@0.417862:0.740495:0.456615:0.740495:0.456615:0.724089:0.417862:0.724089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.440729:0.734431:0.445966:0.734431:0.445966:0.724850:0.440729:0.724850:0.000000 = :@0.456559:0.740495:0.475445:0.740495:0.475445:0.724061:0.456559:0.724061:0.000000:0.000000:0.000000 sen x:@0.475353:0.740495:0.511445:0.740495:0.511445:0.724089:0.475353:0.724089:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.498799:0.734431:0.504036:0.734431:0.504036:0.724850:0.498799:0.724850:0.000000 + :@0.511371:0.740495:0.530257:0.740495:0.530257:0.724061:0.511371:0.724061:0.000000:0.000000:0.000000 senx:@0.530165:0.740495:0.561052:0.740495:0.561052:0.724089:0.530165:0.724089:0.000000:0.000000:0.000000:0.000000 + :@0.561015:0.740495:0.579901:0.740495:0.579901:0.724061:0.561015:0.724061:0.000000:0.000000:0.000000 1:@0.586829:0.733619:0.595812:0.733619:0.595812:0.717185:0.586829:0.717185:0.000000 2 :@0.586829:0.747750:0.599843:0.747750:0.599843:0.731317:0.586829:0.731317:0.000000:0.000000 :@0.602843:0.740497:0.614937:0.740497:0.614937:0.724064:0.602843:0.724064:0.000000:0.000000:0.000000 1 :@0.103215:0.771271:0.125267:0.771271:0.125267:0.754837:0.103215:0.754837:0.000000:0.000000:0.000000 –:@0.112124:0.771853:0.121328:0.771853:0.121328:0.754199:0.112124:0.754199:0.000000 sen x:@0.125194:0.771271:0.161272:0.771266:0.161272:0.754860:0.125194:0.754865:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.148628:0.765202:0.153865:0.765202:0.153865:0.755621:0.148628:0.755621:0.000000 = :@0.161198:0.771266:0.180084:0.771266:0.180084:0.754832:0.161198:0.754832:0.000000:0.000000:0.000000 sen x:@0.179992:0.771266:0.216095:0.771266:0.216095:0.754860:0.179992:0.754860:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.203451:0.765202:0.208688:0.765202:0.208688:0.755621:0.203451:0.755621:0.000000 + :@0.216022:0.771266:0.234908:0.771266:0.234908:0.754832:0.216022:0.754832:0.000000:0.000000:0.000000 senx:@0.234815:0.771266:0.265703:0.771266:0.265703:0.754860:0.234815:0.754860:0.000000:0.000000:0.000000:0.000000 + :@0.265666:0.771266:0.284552:0.771266:0.284552:0.754832:0.265666:0.754832:0.000000:0.000000:0.000000 1:@0.291481:0.764391:0.300464:0.764391:0.300464:0.747957:0.291481:0.747957:0.000000 2 :@0.291481:0.778523:0.304495:0.778523:0.304495:0.762089:0.291481:0.762089:0.000000:0.000000 2:@0.307404:0.771270:0.367835:0.771270:0.367835:0.754836:0.307404:0.754836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sen x:@0.367669:0.771270:0.403767:0.771266:0.403767:0.754860:0.367669:0.754864:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.391122:0.765202:0.396358:0.765202:0.396358:0.755621:0.391122:0.755621:0.000000 + :@0.403694:0.771266:0.422580:0.771266:0.422580:0.754832:0.403694:0.754832:0.000000:0.000000:0.000000 senx:@0.422487:0.771266:0.453375:0.771266:0.453375:0.754860:0.422487:0.754860:0.000000:0.000000:0.000000:0.000000 :@0.453338:0.771266:0.470438:0.771266:0.470438:0.754832:0.453338:0.754832:0.000000:0.000000:0.000000 –:@0.457296:0.771848:0.466499:0.771848:0.466499:0.754194:0.457296:0.754194:0.000000 1:@0.477375:0.764391:0.486357:0.764391:0.486357:0.747957:0.477375:0.747957:0.000000 2 :@0.477375:0.778523:0.490388:0.778523:0.490388:0.762089:0.477375:0.762089:0.000000:0.000000 = 0:@0.493297:0.771270:0.521092:0.771270:0.521092:0.754836:0.493297:0.754836:0.000000:0.000000:0.000000:0.000000 :@0.103210:0.817520:0.107241:0.817520:0.107241:0.801086:0.103210:0.801086:0.000000 senx:@0.107168:0.817520:0.138055:0.817520:0.138055:0.801114:0.107168:0.801114:0.000000:0.000000:0.000000:0.000000 = :@0.138018:0.817520:0.160862:0.817520:0.160862:0.801086:0.138018:0.801086:0.000000:0.000000:0.000000:0.000000 :@0.701364:0.817515:0.761832:0.817515:0.761832:0.801081:0.701364:0.801081:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.103210:0.856203:0.107241:0.856203:0.107241:0.839770:0.103210:0.839770:0.000000 senx:@0.107167:0.856203:0.138055:0.856203:0.138055:0.839797:0.107167:0.839797:0.000000:0.000000:0.000000:0.000000 = :@0.138018:0.856203:0.156904:0.856203:0.156904:0.839770:0.138018:0.839770:0.000000:0.000000:0.000000 0.41143 :@0.253987:0.856203:0.370008:0.856203:0.370008:0.839770:0.253987:0.839770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 senx:@0.369777:0.856203:0.400665:0.856203:0.400665:0.839797:0.369777:0.839797:0.000000:0.000000:0.000000:0.000000 = :@0.400628:0.856203:0.419514:0.856203:0.419514:0.839770:0.400628:0.839770:0.000000:0.000000:0.000000 0.91143:@0.516306:0.856203:0.589983:0.856203:0.589983:0.839770:0.516306:0.839770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.520257:0.856786:0.529460:0.856786:0.529460:0.839132:0.520257:0.839132:0.000000 = :@0.103204:0.883565:0.133428:0.883565:0.133428:0.867132:0.103204:0.867132:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.107161:0.883565:0.114616:0.883565:0.114616:0.867159:0.107161:0.867159:0.000000 sen:@0.133336:0.883565:0.156842:0.883565:0.156842:0.867159:0.133336:0.867159:0.000000:0.000000:0.000000 –:@0.156794:0.877842:0.162160:0.877842:0.162160:0.867550:0.156794:0.867550:0.000000 1:@0.162106:0.877503:0.167343:0.877503:0.167343:0.867922:0.162106:0.867922:0.000000 (0.41143) = :@0.167296:0.883567:0.397957:0.883567:0.397957:0.867133:0.167296:0.867133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.371690:0.883567:0.379145:0.883567:0.379145:0.867161:0.371690:0.867161:0.000000 sen:@0.397865:0.883567:0.421371:0.883567:0.421371:0.867161:0.397865:0.867161:0.000000:0.000000:0.000000 –:@0.421324:0.877842:0.426690:0.877842:0.426690:0.867550:0.421324:0.867550:0.000000 1:@0.426636:0.877503:0.431873:0.877503:0.431873:0.867922:0.426636:0.867922:0.000000 ( 0.91143):@0.431825:0.883567:0.507203:0.883567:0.507203:0.867133:0.431825:0.867133:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 –:@0.436629:0.884149:0.445833:0.884149:0.445833:0.866495:0.436629:0.866495:0.000000 x:@0.103219:0.910929:0.113913:0.910929:0.113913:0.894523:0.103219:0.894523:0.000000:0.000000 = 0.424 = 4.288:@0.113858:0.910929:0.433942:0.910929:0.433942:0.894495:0.113858:0.894495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.368909:0.910929:0.376364:0.910929:0.376364:0.894523:0.368909:0.894523:0.000000 Solución: = 0,424 y = 4,288:@0.073104:0.938291:0.289206:0.938291:0.289206:0.921857:0.073104:0.921857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.143346:0.938291:0.150801:0.938291:0.150801:0.921884:0.143346:0.921884:0.000000 x:@0.224173:0.938291:0.231628:0.938291:0.231628:0.921884:0.224173:0.921884:0.000000 Competencia digital :@0.117786:0.097877:0.407670:0.097877:0.407670:0.069760:0.117786:0.069760:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.200198:0.614894:0.207578:0.614894:0.207578:0.599728:0.200198:0.599728:0.000000 = cos :@0.207578:0.614894:0.251404:0.614894:0.251404:0.599740:0.207578:0.599740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.251404:0.614894:0.258783:0.614894:0.258783:0.599728:0.251404:0.599728:0.000000 y:@0.750140:0.614894:0.757520:0.614894:0.757520:0.599728:0.750140:0.599728:0.000000 = sin :@0.757520:0.614894:0.797965:0.614894:0.797965:0.599740:0.757520:0.599740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x +:@0.797965:0.614894:0.818364:0.614894:0.818364:0.599728:0.797965:0.599728:0.000000:0.000000:0.000000 0.5:@0.818364:0.614894:0.842544:0.614894:0.842544:0.599740:0.818364:0.599740:0.000000:0.000000:0.000000:0.000000 (0.424, 0.911):@0.219770:0.484117:0.311890:0.484117:0.311890:0.468963:0.219770:0.468963:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (4.288, -0.411):@0.464687:0.571600:0.561944:0.571600:0.561944:0.556446:0.464687:0.556446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (2∏, 0):@0.616865:0.540826:0.660841:0.540826:0.660841:0.525671:0.616865:0.525671:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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