﻿72:@0.036727:0.974518:0.057230:0.974518:0.057230:0.956333:0.036727:0.956333:0.000000:0.000000
Trigonometría analítica:@0.073089:0.043661:0.282466:0.043661:0.282466:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tema 2. Funciones trigonométricas inversas y ecuaciones trigonométricas:@0.073089:0.096001:0.924802:0.096001:0.924802:0.070227:0.073089:0.070227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si sen   = :@0.293660:0.174860:0.367903:0.174860:0.367903:0.158426:0.293660:0.158426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.339206:0.174860:0.349091:0.174860:0.349091:0.158454:0.339206:0.158454:0.000000
1:@0.374545:0.167374:0.383528:0.167374:0.383528:0.150940:0.374545:0.150940:0.000000
2 :@0.374545:0.182421:0.387559:0.182421:0.387559:0.165987:0.374545:0.165987:0.000000:0.000000
, encuentra el ángulo   usando la función inversa.:@0.389952:0.174863:0.748713:0.174863:0.748713:0.158429:0.389952:0.158429:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.547095:0.174863:0.556979:0.174863:0.556979:0.158457:0.547095:0.158457:0.000000
Reto matemático:@0.302768:0.139600:0.437491:0.139600:0.437491:0.122653:0.302768:0.122653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.1 Inversa de las funciones sen , cos  y tan:@0.293660:0.234221:0.633274:0.234221:0.633274:0.217274:0.293660:0.217274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.539323:0.234221:0.548012:0.234221:0.548012:0.217274:0.539323:0.217274:0.000000
x:@0.581862:0.234221:0.590551:0.234221:0.590551:0.217274:0.581862:0.217274:0.000000
x:@0.633182:0.234221:0.641870:0.234221:0.641870:0.217274:0.633182:0.217274:0.000000
Las funciones trigonométricas y = :@0.293642:0.261583:0.539456:0.261583:0.539456:0.245149:0.293642:0.245149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
senx y = cosx:@0.538734:0.261583:0.639381:0.261583:0.639381:0.245177:0.538734:0.245177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 e :@0.569401:0.261583:0.585728:0.261583:0.585728:0.245149:0.569401:0.245149:0.000000:0.000000:0.000000
 tienen su dominio en el conjunto de los :@0.639256:0.261583:0.931142:0.261583:0.931142:0.245149:0.639256:0.245149:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales ( ) y sus imágenes están en el intervalo :@0.293642:0.278225:0.631014:0.278225:0.631014:0.261791:0.293642:0.261791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.344114:0.278807:0.357404:0.278807:0.357404:0.261153:0.344114:0.261153:0.000000
. :@0.672199:0.278226:0.679433:0.278226:0.679433:0.261792:0.672199:0.261792:0.000000:0.000000
Al determinar las inversas de las funciones, estas tendrían, ‘como dominio’, el intervalo:@0.293653:0.305588:0.926977:0.305588:0.926977:0.289154:0.293653:0.289154:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 , y como imagen, el conjunto de los números reales ( ), pero sería una relación :@0.335271:0.322231:0.931060:0.322231:0.931060:0.305797:0.335271:0.305797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ℝ:@0.732591:0.322814:0.745881:0.322814:0.745881:0.305160:0.732591:0.305160:0.000000
inversa. :@0.293652:0.338873:0.351659:0.338873:0.351659:0.322439:0.293652:0.322439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Así que hay que restringir los dominios de las funciones trigonométricas   = :@0.293652:0.366235:0.880171:0.366235:0.880171:0.349801:0.293652:0.349801:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.851870:0.366235:0.859343:0.366235:0.859343:0.349829:0.851870:0.349829:0.000000
senx:@0.881635:0.366235:0.913185:0.366235:0.913185:0.349829:0.881635:0.349829:0.000000:0.000000:0.000000:0.000000
 y :@0.913332:0.366235:0.930957:0.366235:0.930957:0.349801:0.913332:0.349801:0.000000:0.000000:0.000000
y:@0.293670:0.382877:0.301144:0.382877:0.301144:0.366471:0.293670:0.366471:0.000000
 = :@0.301331:0.382878:0.320843:0.382878:0.320843:0.366444:0.301331:0.366444:0.000000:0.000000:0.000000
cosx:@0.321085:0.382878:0.352258:0.382878:0.352258:0.366472:0.321085:0.366472:0.000000:0.000000:0.000000:0.000000
 para que sus inversas sean funciones. Igual pasa con las demás funciones :@0.352451:0.382878:0.930829:0.382878:0.930829:0.366444:0.352451:0.366444:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométricas. :@0.293658:0.399520:0.416652:0.399520:0.416652:0.383086:0.293658:0.383086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función inversa del seno:@0.293658:0.426882:0.480350:0.426882:0.480350:0.410212:0.293658:0.410212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función inversa del seno se define como la función sen  de dominio :@0.293658:0.460290:0.824443:0.460298:0.824443:0.443864:0.293658:0.443857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.719740:0.454574:0.725105:0.454574:0.725105:0.444281:0.719740:0.444281:0.000000
1:@0.725105:0.454234:0.730342:0.454234:0.730342:0.444653:0.725105:0.444653:0.000000
 y rango :@0.866454:0.460298:0.930934:0.460298:0.930934:0.443864:0.866454:0.443864:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y la notamos como :@0.362617:0.482991:0.510114:0.482991:0.510114:0.466558:0.362617:0.466558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y = sen x:@0.509912:0.482991:0.576126:0.482991:0.576126:0.466585:0.509912:0.466585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.558169:0.477267:0.563535:0.477267:0.563535:0.466975:0.558169:0.466975:0.000000
1:@0.563481:0.476927:0.568718:0.476927:0.568718:0.467347:0.563481:0.467347:0.000000
 que equivale a :@0.576052:0.482991:0.690141:0.482991:0.690141:0.466558:0.576052:0.466558:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x = seny:@0.689957:0.482991:0.745620:0.482991:0.745620:0.466585:0.689957:0.466585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. :@0.745602:0.482991:0.752836:0.482991:0.752836:0.466558:0.745602:0.466558:0.000000:0.000000
A la función inversa del seno, también se le da el nombre de arcoseno y la notamos :@0.293648:0.517495:0.930838:0.517495:0.930838:0.501062:0.293648:0.501062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como   = :@0.293648:0.534137:0.366431:0.534137:0.366431:0.517704:0.293648:0.517704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.340145:0.534137:0.347618:0.534137:0.347618:0.517731:0.340145:0.517731:0.000000
arco senx:@0.366339:0.534137:0.432016:0.534137:0.432016:0.517731:0.366339:0.517731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.397171:0.534137:0.401202:0.534137:0.401202:0.517704:0.397171:0.517704:0.000000
.:@0.431979:0.534137:0.435182:0.534137:0.435182:0.517704:0.431979:0.517704:0.000000
La expresión :@0.293667:0.561499:0.389230:0.561499:0.389230:0.545065:0.293667:0.545065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
arco senx:@0.389348:0.561499:0.455301:0.561499:0.455301:0.545093:0.389348:0.545093:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.420180:0.561499:0.424211:0.561499:0.424211:0.545065:0.420180:0.545065:0.000000
 hace referencia a encontrar el arco (en la circunferencia unitaria), :@0.455264:0.561499:0.931342:0.561499:0.931342:0.545065:0.455264:0.545065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cuyo seno da como resultado  .:@0.293685:0.578141:0.523150:0.578141:0.523150:0.561707:0.293685:0.561707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.512566:0.578141:0.520021:0.578141:0.520021:0.561735:0.512566:0.561735:0.000000
Gráfica de   = :@0.293667:0.616223:0.396582:0.616223:0.396582:0.599789:0.293667:0.599789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.370296:0.616223:0.377770:0.616223:0.377770:0.599817:0.370296:0.599817:0.000000
sen x  arc senx:@0.396490:0.616223:0.516565:0.616233:0.516565:0.599827:0.396490:0.599817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.419937:0.610509:0.425303:0.610509:0.425303:0.600216:0.419937:0.600216:0.000000
1:@0.425249:0.610169:0.430486:0.610169:0.430486:0.600588:0.425249:0.600588:0.000000
  = :@0.430438:0.616233:0.459963:0.616233:0.459963:0.599799:0.430438:0.599799:0.000000:0.000000:0.000000:0.000000
 :@0.481720:0.616233:0.485752:0.616233:0.485752:0.599799:0.481720:0.599799:0.000000
y:@0.357224:0.638969:0.362257:0.638969:0.362257:0.627918:0.357224:0.627918:0.000000
p:@0.352756:0.764741:0.362863:0.764741:0.362863:0.753450:0.352756:0.753450:0.000000
2:@0.355119:0.776647:0.361169:0.776647:0.361169:0.765578:0.355119:0.765578:0.000000
p:@0.352677:0.649998:0.362784:0.649998:0.362784:0.638707:0.352677:0.638707:0.000000
2:@0.355042:0.661904:0.361092:0.661904:0.361092:0.650835:0.355042:0.650835:0.000000
0:@0.372833:0.721489:0.378883:0.721489:0.378883:0.710420:0.372833:0.710420:0.000000
1:@0.416796:0.722395:0.422846:0.722395:0.422846:0.711326:0.416796:0.711326:0.000000
1:@0.318059:0.722395:0.324109:0.722395:0.324109:0.711326:0.318059:0.711326:0.000000
x:@0.452328:0.721068:0.457349:0.721068:0.457349:0.710018:0.452328:0.710018:0.000000
y = :@0.390024:0.646311:0.406910:0.646311:0.406910:0.635261:0.390024:0.635261:0.000000:0.000000:0.000000:0.000000
sen:@0.406910:0.646311:0.424192:0.646311:0.424192:0.635242:0.406910:0.635242:0.000000:0.000000:0.000000
_:@0.424193:0.639825:0.429703:0.639825:0.429703:0.629986:0.424193:0.629986:0.000000
1:@0.429703:0.642938:0.435081:0.642938:0.435081:0.633099:0.429703:0.633099:0.000000
x:@0.435080:0.646311:0.440101:0.646311:0.440101:0.635261:0.435080:0.635261:0.000000
               :@0.466931:0.784921:0.526368:0.784921:0.526368:0.768487:0.466931:0.768487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.635689:0.642386:0.641803:0.642386:0.641803:0.628963:0.635689:0.628963:0.000000
p:@0.576864:0.684556:0.589142:0.684556:0.589142:0.670840:0.576864:0.670840:0.000000
2:@0.579736:0.699019:0.587085:0.699019:0.587085:0.685573:0.579736:0.685573:0.000000
p:@0.715583:0.727244:0.727860:0.727244:0.727860:0.713529:0.715583:0.713529:0.000000
2:@0.718454:0.741708:0.725804:0.741708:0.725804:0.728262:0.718454:0.728262:0.000000
0:@0.657926:0.721556:0.665276:0.721556:0.665276:0.708110:0.657926:0.708110:0.000000
1:@0.633589:0.680333:0.640938:0.680333:0.640938:0.666887:0.633589:0.666887:0.000000
x:@0.774924:0.722479:0.781024:0.722479:0.781024:0.709056:0.774924:0.709056:0.000000
y:@0.293660:0.812284:0.301133:0.812284:0.301133:0.795878:0.293660:0.795878:0.000000
 = :@0.301060:0.812284:0.319946:0.812284:0.319946:0.795850:0.301060:0.795850:0.000000:0.000000:0.000000
senx:@0.319854:0.812284:0.350741:0.812284:0.350741:0.795878:0.319854:0.795878:0.000000:0.000000:0.000000:0.000000
 :@0.350701:0.812284:0.354732:0.812284:0.354732:0.795850:0.350701:0.795850:0.000000
y:@0.529608:0.812284:0.537081:0.812284:0.537081:0.795878:0.529608:0.795878:0.000000
 = :@0.537007:0.812284:0.555893:0.812284:0.555893:0.795850:0.537007:0.795850:0.000000:0.000000:0.000000
sen x:@0.555801:0.812284:0.597224:0.812284:0.597224:0.795878:0.555801:0.795878:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.579259:0.806220:0.584624:0.806220:0.584624:0.796502:0.579259:0.796502:0.000000
1:@0.584581:0.806220:0.589818:0.806220:0.589818:0.796639:0.584581:0.796639:0.000000
Dominio = :@0.293652:0.835874:0.376256:0.835874:0.376256:0.819440:0.293652:0.819440:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.445087:0.835876:0.449118:0.835876:0.449118:0.819443:0.445087:0.819443:0.000000
Dominio = :@0.529613:0.835876:0.612224:0.835876:0.612224:0.819443:0.529613:0.819443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Imagen = :@0.293660:0.864828:0.368497:0.864828:0.368497:0.848394:0.293660:0.848394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.409867:0.864828:0.413898:0.864828:0.413898:0.848394:0.409867:0.848394:0.000000
Imagen = :@0.529606:0.864828:0.604395:0.864828:0.604395:0.848394:0.529606:0.848394:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Fuente: imagenes tomadas del :@0.293660:0.895765:0.520528:0.895765:0.520528:0.879332:0.293660:0.879332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Precálculo :@0.520272:0.895765:0.594641:0.895765:0.594641:0.879359:0.520272:0.879359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de James Stewart:@0.594619:0.895765:0.722483:0.895765:0.722483:0.879332:0.594619:0.879332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una función tiene inversa :@0.078581:0.399141:0.250242:0.399141:0.250242:0.384201:0.078581:0.384201:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si es biyectiva.:@0.078581:0.414269:0.171474:0.414269:0.171474:0.399330:0.078581:0.399330:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Las funciones :@0.078581:0.436547:0.171872:0.436547:0.171872:0.421607:0.078581:0.421607:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométricas no son :@0.078581:0.451676:0.236585:0.451676:0.236585:0.436736:0.078581:0.436736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
biyectivas y, por tanto, :@0.078581:0.466805:0.228587:0.466805:0.228587:0.451865:0.078581:0.451865:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
no tienen inversas; lo :@0.078581:0.481934:0.220774:0.481934:0.220774:0.466994:0.078581:0.466994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que nos lleva a hacer una :@0.078581:0.497063:0.249710:0.497063:0.249710:0.482123:0.078581:0.482123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
restricción en sus dominios :@0.078581:0.512192:0.261889:0.512192:0.261889:0.497252:0.078581:0.497252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a uno en los que alcancen :@0.078581:0.527320:0.254889:0.527320:0.254889:0.512381:0.078581:0.512381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
todos sus valores y en los :@0.078581:0.542449:0.248333:0.542449:0.248333:0.527510:0.078581:0.527510:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que forman una biyección.:@0.078581:0.557578:0.255130:0.557578:0.255130:0.542639:0.078581:0.542639:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Una observación: las :@0.078581:0.579856:0.217566:0.579856:0.217566:0.564916:0.078581:0.564916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nuevas funciones tendrán :@0.078581:0.594985:0.253654:0.594985:0.253654:0.580045:0.078581:0.580045:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el mismo conjunto imagen :@0.078581:0.610114:0.261132:0.610114:0.261132:0.595174:0.078581:0.595174:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de las funciones originales.:@0.078581:0.625243:0.254902:0.625243:0.254902:0.610303:0.078581:0.610303:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.078581:0.358434:0.187141:0.358434:0.187141:0.341487:0.078581:0.341487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078581:0.375075:0.176057:0.375075:0.176057:0.358128:0.078581:0.358128:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 4 (Ev. 4) Reconoce algunas aplicaciones de las funciones trigonométricas en el estudio de fenómenos diversos de :@0.262462:0.966318:0.887146:0.966318:0.887146:0.954366:0.262462:0.954366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variación periódica, por ejemplo: movimiento circular, movimiento del péndulo, del pistón, ciclo de la respiración, entre otros.:@0.262462:0.976404:0.921175:0.976404:0.921175:0.964452:0.262462:0.964452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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