81:@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
Metacognición:@0.104317:0.866410:0.205175:0.866410:0.205175:0.851471:0.104317:0.851471:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.104317:0.885850:0.116952:0.885850:0.116952:0.872404:0.104317:0.872404:0.000000:0.000000:0.000000
¿Cuál es el proceso general para demostrar una identidad trigonométrica y qué herramientas matemáticas se deben dominar :@0.134437:0.885850:0.881321:0.885850:0.881321:0.872404:0.134437:0.872404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
para lograrlo?:@0.134437:0.898456:0.215436:0.898456:0.215436:0.885010:0.134437:0.885010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b. :@0.104317:0.911065:0.118142:0.911065:0.118142:0.897619:0.104317:0.897619:0.000000:0.000000:0.000000
En qué situaciones en la vida real es útil conocer las identidades de suma y producto en trigonometría, como las que :@0.134437:0.911065:0.828730:0.911065:0.828730:0.897619:0.134437:0.897619:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
transforman una suma en un producto?:@0.134437:0.923671:0.371071:0.923671:0.371071:0.910226:0.134437:0.910226:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c. :@0.104317:0.936280:0.116651:0.936280:0.116651:0.922834:0.104317:0.922834:0.000000:0.000000:0.000000
¿Cuál es la relación entre las identidades de cofunciones y los ángulos complementarios, y cómo puedes usarlas para simplificar :@0.134437:0.936280:0.893858:0.936280:0.893858:0.922834:0.134437:0.922834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cálculos trigonométricos?:@0.134437:0.948886:0.287274:0.948886:0.287274:0.935441:0.134437:0.935441:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Coevaluació:@0.133568:0.705509:0.226294:0.705509:0.226294:0.688840:0.133568:0.688840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.226181:0.705194:0.235468:0.705194:0.235468:0.690040:0.226181:0.690040:0.000000
Autoevaluación:@0.131196:0.523632:0.250610:0.523632:0.250610:0.506962:0.131196:0.506962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Siempre:@0.662567:0.546394:0.728148:0.546394:0.728148:0.529447:0.662567:0.529447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A veces:@0.750480:0.546394:0.809434:0.546394:0.809434:0.529447:0.750480:0.529447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nunca:@0.831600:0.546394:0.882368:0.546394:0.882368:0.529447:0.831600:0.529447:0.000000:0.000000:0.000000:0.000000:0.000000
Describo y modelo fenómenos periódicos del mundo real, usando relaciones y :@0.119021:0.567381:0.588694:0.567381:0.588694:0.553935:0.119021:0.553935:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones trigonométricas.:@0.119021:0.579987:0.277936:0.579987:0.277936:0.566541:0.119021:0.566541:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Utilizo relaciones trigonométricas para determinar longitudes y medidas de ángulos.:@0.119021:0.598584:0.619171:0.598584:0.619171:0.585138:0.119021:0.585138:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconozco las funciones trigonométricas inversas, construyo sus gráficas en el plano :@0.119021:0.619076:0.642594:0.619076:0.642594:0.605630:0.119021:0.605630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cartesiano y deduzco sus propiedades principales.:@0.119021:0.631682:0.415925:0.631682:0.415925:0.618237:0.119021:0.618237:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconozco las identidades trigonométricas fundamentales y deduzco otras identidades a :@0.119021:0.650280:0.642216:0.650280:0.642216:0.636834:0.119021:0.636834:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
partir de estas.:@0.119021:0.662886:0.202655:0.662886:0.202655:0.649440:0.119021:0.649440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
11.  ¿Cuál de las siguientes es una identidad :@0.073089:0.136836:0.407134:0.136836:0.407134:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométrica verdadera::@0.103214:0.153478:0.301917:0.153478:0.301917:0.136808:0.103214:0.136808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.104633:0.178340:0.120077:0.178340:0.120077:0.161906:0.104633:0.161906:0.000000:0.000000:0.000000
sin x:@0.134834:0.178340:0.171744:0.178340:0.171744:0.161934:0.134834:0.161934:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.154295:0.172276:0.159532:0.172276:0.159532:0.162695:0.154295:0.162695:0.000000
( ) + :@0.159485:0.178340:0.195360:0.178340:0.195360:0.161906:0.159485:0.161906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.195250:0.178340:0.235574:0.178340:0.235574:0.161934:0.195250:0.161934:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.218125:0.172276:0.223362:0.172276:0.223362:0.162695:0.218125:0.162695:0.000000
( ) = 2:@0.223314:0.178340:0.268099:0.178340:0.268099:0.161906:0.223314:0.161906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b. :@0.104633:0.203201:0.121531:0.203201:0.121531:0.186767:0.104633:0.186767:0.000000:0.000000:0.000000
sin x:@0.134834:0.203201:0.171744:0.203201:0.171744:0.186795:0.134834:0.186795:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.154295:0.197137:0.159532:0.197137:0.159532:0.187556:0.154295:0.187556:0.000000
( ) + :@0.159485:0.203201:0.195360:0.203201:0.195360:0.186767:0.159485:0.186767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.195250:0.203201:0.235574:0.203201:0.235574:0.186795:0.195250:0.186795:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.218125:0.197137:0.223362:0.197137:0.223362:0.187556:0.218125:0.187556:0.000000
( ) = 1:@0.223314:0.203201:0.268099:0.203201:0.268099:0.186767:0.223314:0.186767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c. :@0.104633:0.228062:0.119708:0.228062:0.119708:0.211629:0.104633:0.211629:0.000000:0.000000:0.000000
sin x:@0.134834:0.228062:0.171744:0.228062:0.171744:0.211656:0.134834:0.211656:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.154295:0.221999:0.159532:0.221999:0.159532:0.212418:0.154295:0.212418:0.000000
( ) + :@0.159485:0.228062:0.195360:0.228062:0.195360:0.211629:0.159485:0.211629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.195250:0.228062:0.235574:0.228062:0.235574:0.211656:0.195250:0.211656:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.218125:0.221999:0.223362:0.221999:0.223362:0.212418:0.218125:0.212418:0.000000
( ) = :@0.223314:0.228062:0.259190:0.228062:0.259190:0.211629:0.223314:0.211629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tan x:@0.259080:0.228062:0.300471:0.228062:0.300471:0.211656:0.259080:0.211656:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.283022:0.221999:0.288259:0.221999:0.288259:0.212418:0.283022:0.212418:0.000000
( ):@0.288212:0.228062:0.305275:0.228062:0.305275:0.211629:0.288212:0.211629:0.000000:0.000000:0.000000
d. :@0.104633:0.252924:0.121512:0.252924:0.121512:0.236491:0.104633:0.236491:0.000000:0.000000:0.000000
sin x:@0.134834:0.252924:0.171744:0.252924:0.171744:0.236518:0.134834:0.236518:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.154295:0.246860:0.159532:0.246860:0.159532:0.237280:0.154295:0.237280:0.000000
( ) + :@0.159485:0.252924:0.195360:0.252924:0.195360:0.236491:0.159485:0.236491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.195250:0.252924:0.235574:0.252924:0.235574:0.236518:0.195250:0.236518:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.218125:0.246860:0.223362:0.246860:0.223362:0.237280:0.218125:0.237280:0.000000
( ) = :@0.223314:0.252924:0.259190:0.252924:0.259190:0.236491:0.223314:0.236491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sec x:@0.259080:0.252924:0.298151:0.252924:0.298151:0.236518:0.259080:0.236518:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.280703:0.246860:0.285940:0.246860:0.285940:0.237280:0.280703:0.237280:0.000000
( ):@0.285892:0.252924:0.302956:0.252924:0.302956:0.236491:0.285892:0.236491:0.000000:0.000000:0.000000
12.  ¿Cuál es la solución de la ecuación sin( ) = :@0.073089:0.289067:0.422893:0.289067:0.422893:0.272398:0.073089:0.272398:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.391251:0.289067:0.399368:0.289067:0.399368:0.272384:0.391251:0.272384:0.000000
3:@0.432906:0.278250:0.441889:0.278250:0.441889:0.261816:0.432906:0.261816:0.000000
2 :@0.429363:0.294847:0.442377:0.294847:0.442377:0.278413:0.429363:0.278413:0.000000:0.000000
en el :@0.449354:0.289064:0.489684:0.289064:0.489684:0.272394:0.449354:0.272394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intervalo 0 < x < 2 ?:@0.103205:0.305705:0.258489:0.305705:0.258489:0.289036:0.103205:0.289036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.238830:0.305151:0.251108:0.305151:0.251108:0.291435:0.238830:0.291435:0.000000
a. :@0.104633:0.333979:0.120077:0.333979:0.120077:0.317545:0.104633:0.317545:0.000000:0.000000:0.000000
p:@0.140214:0.325856:0.152492:0.325856:0.152492:0.312140:0.140214:0.312140:0.000000
3 :@0.141871:0.340542:0.154884:0.340542:0.154884:0.324109:0.141871:0.324109:0.000000:0.000000
b. :@0.104633:0.371898:0.121531:0.371898:0.121531:0.355465:0.104633:0.355465:0.000000:0.000000:0.000000
2:@0.135763:0.365024:0.144745:0.365024:0.144745:0.348590:0.135763:0.348590:0.000000
p:@0.144672:0.364469:0.156949:0.364469:0.156949:0.350753:0.144672:0.350753:0.000000
3 :@0.141874:0.379155:0.154888:0.379155:0.154888:0.362721:0.141874:0.362721:0.000000:0.000000
c. :@0.104633:0.409818:0.119708:0.409818:0.119708:0.393384:0.104633:0.393384:0.000000:0.000000:0.000000
p:@0.140214:0.401694:0.152492:0.401694:0.152492:0.387978:0.140214:0.387978:0.000000
3 :@0.141871:0.416380:0.154884:0.416380:0.154884:0.399946:0.141871:0.399946:0.000000:0.000000
 y :@0.157793:0.409820:0.173807:0.409820:0.173807:0.393386:0.157793:0.393386:0.000000:0.000000:0.000000
2:@0.174639:0.402942:0.183622:0.402942:0.183622:0.386508:0.174639:0.386508:0.000000
p:@0.183548:0.402387:0.195826:0.402387:0.195826:0.388671:0.183548:0.388671:0.000000
3 :@0.180750:0.417073:0.193764:0.417073:0.193764:0.400640:0.180750:0.400640:0.000000:0.000000
d. :@0.104633:0.447737:0.121512:0.447737:0.121512:0.431303:0.104633:0.431303:0.000000:0.000000:0.000000
5:@0.135763:0.440861:0.144745:0.440861:0.144745:0.424427:0.135763:0.424427:0.000000
p:@0.144672:0.440306:0.156949:0.440306:0.156949:0.426591:0.144672:0.426591:0.000000
3 :@0.141874:0.454993:0.154888:0.454993:0.154888:0.438559:0.141874:0.438559:0.000000:0.000000
13.  ¿Cuál de las siguientes es una identidad verdadera?:@0.514231:0.136836:0.926886:0.136836:0.926886:0.120167:0.514231:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.545774:0.160625:0.561218:0.160625:0.561218:0.144191:0.545774:0.144191:0.000000:0.000000:0.000000
sec x:@0.575976:0.160625:0.615039:0.160625:0.615039:0.144219:0.575976:0.144219:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.597591:0.154561:0.602828:0.154561:0.602828:0.144980:0.597591:0.144980:0.000000
( ) = 1 + :@0.602780:0.160625:0.666377:0.160625:0.666377:0.144191:0.602780:0.144191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cot x:@0.666248:0.160625:0.705568:0.160625:0.705568:0.144219:0.666248:0.144219:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.688119:0.154561:0.693356:0.154561:0.693356:0.144980:0.688119:0.144980:0.000000
( ):@0.693308:0.160625:0.710372:0.160625:0.710372:0.144191:0.693308:0.144191:0.000000:0.000000:0.000000
b. :@0.545774:0.184415:0.562672:0.184415:0.562672:0.167982:0.545774:0.167982:0.000000:0.000000:0.000000
sec x:@0.575976:0.184415:0.615039:0.184415:0.615039:0.168009:0.575976:0.168009:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.597591:0.178352:0.602828:0.178352:0.602828:0.168771:0.597591:0.168771:0.000000
( ) = 1 + :@0.602780:0.184415:0.666377:0.184415:0.666377:0.167982:0.602780:0.167982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tag x:@0.666248:0.184415:0.707390:0.184415:0.707390:0.168009:0.666248:0.168009:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.689942:0.178352:0.695178:0.178352:0.695178:0.168771:0.689942:0.168771:0.000000
( ):@0.695131:0.184415:0.712194:0.184415:0.712194:0.167982:0.695131:0.167982:0.000000:0.000000:0.000000
c. :@0.545774:0.208204:0.560850:0.208204:0.560850:0.191771:0.545774:0.191771:0.000000:0.000000:0.000000
sec x:@0.575976:0.208204:0.615039:0.208204:0.615039:0.191798:0.575976:0.191798:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.597591:0.202141:0.602828:0.202141:0.602828:0.192560:0.597591:0.192560:0.000000
( ) = :@0.602780:0.208204:0.638656:0.208204:0.638656:0.191771:0.602780:0.191771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sin x:@0.638545:0.208204:0.675463:0.208204:0.675463:0.191798:0.638545:0.191798:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.658015:0.202141:0.663252:0.202141:0.663252:0.192560:0.658015:0.192560:0.000000
( ) + :@0.663204:0.208204:0.699080:0.208204:0.699080:0.191771:0.663204:0.191771:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.698969:0.208204:0.739293:0.208204:0.739293:0.191798:0.698969:0.191798:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.721845:0.202141:0.727082:0.202141:0.727082:0.192560:0.721845:0.192560:0.000000
( ):@0.727034:0.208204:0.744097:0.208204:0.744097:0.191771:0.727034:0.191771:0.000000:0.000000:0.000000
d. :@0.545774:0.231993:0.562654:0.231993:0.562654:0.215560:0.545774:0.215560:0.000000:0.000000:0.000000
sec x:@0.575976:0.231993:0.615039:0.231993:0.615039:0.215587:0.575976:0.215587:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.597591:0.225930:0.602828:0.225930:0.602828:0.216349:0.597591:0.216349:0.000000
( ) = :@0.602780:0.231993:0.638656:0.231993:0.638656:0.215560:0.602780:0.215560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sin x:@0.638545:0.231993:0.675463:0.231993:0.675463:0.215587:0.638545:0.215587:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.658015:0.225930:0.663252:0.225930:0.663252:0.216349:0.658015:0.216349:0.000000
( ) + 1:@0.663204:0.231993:0.707989:0.231993:0.707989:0.215560:0.663204:0.215560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
14.  ¿Cuál de las siguientes es una identidad verdadera?:@0.514231:0.255782:0.926886:0.255782:0.926886:0.239113:0.514231:0.239113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a. :@0.545774:0.279573:0.561218:0.279573:0.561218:0.263139:0.545774:0.263139:0.000000:0.000000:0.000000
sin x:@0.575976:0.279573:0.616582:0.279573:0.616582:0.263167:0.575976:0.263167:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ) = 2:@0.595432:0.279573:0.649108:0.279573:0.649108:0.263139:0.595432:0.263139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sin x cos x:@0.648997:0.279573:0.724504:0.279573:0.724504:0.263167:0.648997:0.263167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
( ) :@0.668454:0.279573:0.689475:0.279573:0.689475:0.263139:0.668454:0.263139:0.000000:0.000000:0.000000:0.000000
( ):@0.712244:0.279573:0.729308:0.279573:0.729308:0.263139:0.712244:0.263139:0.000000:0.000000:0.000000
b. :@0.545774:0.303362:0.562672:0.303362:0.562672:0.286928:0.545774:0.286928:0.000000:0.000000:0.000000
sin x:@0.575976:0.303362:0.616582:0.303362:0.616582:0.286956:0.575976:0.286956:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ) = :@0.595432:0.303362:0.640198:0.303362:0.640198:0.286928:0.595432:0.286928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sin x:@0.640088:0.303362:0.677023:0.303362:0.677023:0.286956:0.640088:0.286956:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.659573:0.297298:0.664810:0.297298:0.664810:0.287717:0.659573:0.287717:0.000000
( ) + :@0.664764:0.303362:0.700639:0.303362:0.700639:0.286928:0.664764:0.286928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.700529:0.303362:0.740853:0.303362:0.740853:0.286956:0.700529:0.286956:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.723403:0.297298:0.728639:0.297298:0.728639:0.287717:0.723403:0.287717:0.000000
( ):@0.728593:0.303362:0.745657:0.303362:0.745657:0.286928:0.728593:0.286928:0.000000:0.000000:0.000000
c. :@0.545774:0.327151:0.560850:0.327151:0.560850:0.310717:0.545774:0.310717:0.000000:0.000000:0.000000
sin x:@0.575976:0.327151:0.616582:0.327151:0.616582:0.310745:0.575976:0.310745:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ) = 2:@0.595432:0.327151:0.649108:0.327151:0.649108:0.310717:0.595432:0.310717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sin x:@0.648997:0.327151:0.685924:0.327151:0.685924:0.310745:0.648997:0.310745:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.668475:0.321087:0.673712:0.321087:0.673712:0.311506:0.668475:0.311506:0.000000
( )   1:@0.673664:0.327151:0.716645:0.327151:0.716645:0.310717:0.673664:0.310717:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.694594:0.327733:0.703797:0.327733:0.703797:0.310079:0.694594:0.310079:0.000000
d. :@0.545774:0.350941:0.562654:0.350941:0.562654:0.334507:0.545774:0.334507:0.000000:0.000000:0.000000
sin x:@0.575976:0.350941:0.616582:0.350941:0.616582:0.334535:0.575976:0.334535:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ) = :@0.595432:0.350941:0.640198:0.350941:0.640198:0.334507:0.595432:0.334507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cos x:@0.640088:0.350941:0.680428:0.350941:0.680428:0.334535:0.640088:0.334535:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.662978:0.344877:0.668215:0.344877:0.668215:0.335296:0.662978:0.335296:0.000000
( )   :@0.668169:0.350941:0.702241:0.350941:0.702241:0.334507:0.668169:0.334507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.689098:0.351523:0.698302:0.351523:0.698302:0.333869:0.689098:0.333869:0.000000
sin x:@0.702167:0.350941:0.742774:0.350941:0.742774:0.334535:0.702167:0.334535:0.000000:0.000000:0.000000:0.000000:0.000000
2( ):@0.721624:0.350941:0.747578:0.350941:0.747578:0.334507:0.721624:0.334507:0.000000:0.000000:0.000000:0.000000
15.  ¿Cuál es el valor de cos ( ) - sin ( )?:@0.514231:0.374730:0.806583:0.374730:0.806583:0.358060:0.514231:0.358060:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.716689:0.368666:0.722194:0.368666:0.722194:0.358948:0.716689:0.358948:0.000000
x:@0.727303:0.374730:0.735421:0.374730:0.735421:0.358047:0.727303:0.358047:0.000000
2:@0.775299:0.368666:0.780805:0.368666:0.780805:0.358948:0.775299:0.358948:0.000000
x:@0.785912:0.374730:0.794030:0.374730:0.794030:0.358047:0.785912:0.358047:0.000000
a. :@0.545774:0.398519:0.561218:0.398519:0.561218:0.382085:0.545774:0.382085:0.000000:0.000000:0.000000
cos x:@0.575976:0.398519:0.619987:0.398519:0.619987:0.382113:0.575976:0.382113:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ):@0.598837:0.398519:0.624792:0.398519:0.624792:0.382085:0.598837:0.382085:0.000000:0.000000:0.000000:0.000000
b. :@0.545774:0.422309:0.562672:0.422309:0.562672:0.405875:0.545774:0.405875:0.000000:0.000000:0.000000
sin x:@0.575976:0.422309:0.616582:0.422309:0.616582:0.405903:0.575976:0.405903:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ):@0.595432:0.422309:0.621386:0.422309:0.621386:0.405875:0.595432:0.405875:0.000000:0.000000:0.000000:0.000000
c. :@0.545774:0.446098:0.560850:0.446098:0.560850:0.429664:0.545774:0.429664:0.000000:0.000000:0.000000
tan x:@0.575976:0.446098:0.621055:0.446098:0.621055:0.429692:0.575976:0.429692:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ):@0.599905:0.446098:0.625859:0.446098:0.625859:0.429664:0.599905:0.429664:0.000000:0.000000:0.000000:0.000000
d. :@0.545774:0.469887:0.562654:0.469887:0.562654:0.453453:0.545774:0.453453:0.000000:0.000000:0.000000
sec x:@0.575976:0.469887:0.618736:0.469887:0.618736:0.453481:0.575976:0.453481:0.000000:0.000000:0.000000:0.000000:0.000000
(2 ):@0.597586:0.469887:0.623540:0.469887:0.623540:0.453453:0.597586:0.453453:0.000000:0.000000:0.000000:0.000000
Siempre:@0.662172:0.729067:0.727753:0.729067:0.727753:0.712120:0.662172:0.712120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A veces:@0.750085:0.729067:0.809039:0.729067:0.809039:0.712120:0.750085:0.712120:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Nunca:@0.831205:0.729067:0.881973:0.729067:0.881973:0.712120:0.831205:0.712120:0.000000:0.000000:0.000000:0.000000:0.000000
Describo y modelo fenómenos periódicos del mundo real usando relaciones y :@0.118626:0.750054:0.585909:0.750054:0.585909:0.736608:0.118626:0.736608:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones trigonométricas.:@0.118626:0.762660:0.277541:0.762660:0.277541:0.749214:0.118626:0.749214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Utilizo relaciones trigonométricas para determinar longitudes y medidas de ángulos.:@0.118626:0.781257:0.618776:0.781257:0.618776:0.767811:0.118626:0.767811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconozco las funciones trigonométricas inversas, construyo sus gráficas en el plano :@0.118626:0.801749:0.642199:0.801749:0.642199:0.788304:0.118626:0.788304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cartesiano y deduzco sus propiedades principales.:@0.118626:0.814356:0.415530:0.814356:0.415530:0.800910:0.118626:0.800910:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reconozco las identidades trigonométricas fundamentales y deduzco otras identidades a :@0.118626:0.832953:0.641821:0.832953:0.641821:0.819507:0.118626:0.819507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
partir de estas.:@0.118626:0.845559:0.202260:0.845559:0.202260:0.832113:0.118626:0.832113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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