174:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Transformaciones de las gráficas de funciones trigonométricas:@0.404235:0.105525:0.891806:0.105525:0.891806:0.087843:0.404235:0.087843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Funciones sinusoidales:@0.404235:0.123630:0.586845:0.123630:0.586845:0.105948:0.404235:0.105948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sean  ,  ,  ,       con   ≠ 0,   ≠ 0 funciones reales definidas como: :@0.404235:0.140338:0.895951:0.140338:0.895951:0.123840:0.404235:0.123840:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C D:@0.441917:0.140454:0.504395:0.140454:0.504395:0.123985:0.441917:0.123985:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.508376:0.139819:0.523028:0.139819:0.523028:0.126446:0.508376:0.126446:0.000000
R:@0.527054:0.139369:0.540963:0.139369:0.540963:0.125922:0.527054:0.125922:0.000000
A:@0.575949:0.140454:0.587219:0.140454:0.587219:0.123985:0.575949:0.123985:0.000000
B:@0.621348:0.140454:0.630537:0.140454:0.630537:0.123985:0.621348:0.123985:0.000000
 :@0.891809:0.140338:0.895951:0.140338:0.895951:0.123840:0.891809:0.123840:0.000000
y Asen Bx C:@0.450532:0.164933:0.563446:0.164933:0.563446:0.148464:0.450532:0.148464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 = :@0.458219:0.164817:0.477311:0.164817:0.477311:0.148319:0.458219:0.148319:0.000000:0.000000:0.000000
(  +  ) +  ;      = :@0.511699:0.164817:0.646229:0.164817:0.646229:0.148319:0.511699:0.148319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.588491:0.164933:0.600127:0.164933:0.600127:0.148464:0.588491:0.148464:0.000000
y Acos Bx C:@0.619450:0.164933:0.730822:0.164933:0.730822:0.148464:0.619450:0.148464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(  +  ) +  ,         .:@0.679076:0.164817:0.845473:0.164816:0.845473:0.148319:0.679076:0.148319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.755867:0.164933:0.767504:0.164933:0.767504:0.148464:0.755867:0.148464:0.000000
∀:@0.786817:0.172403:0.798390:0.172403:0.798390:0.153404:0.786817:0.153404:0.000000
x:@0.798398:0.164932:0.805873:0.164932:0.805873:0.148463:0.798398:0.148463:0.000000
:@0.810014:0.164298:0.824667:0.164298:0.824667:0.150925:0.810014:0.150925:0.000000
R:@0.828808:0.163848:0.842718:0.163848:0.842718:0.150401:0.828808:0.150401:0.000000
Características:@0.404235:0.199565:0.507225:0.199565:0.507225:0.183577:0.404235:0.183577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Amplitud |A|:@0.404235:0.217331:0.506494:0.217331:0.506494:0.200385:0.404235:0.200385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, con   ≠ 0, es el promedio entre los valores máximo y :@0.506398:0.216869:0.895884:0.216869:0.895884:0.200371:0.506398:0.200371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.545160:0.216984:0.556430:0.216984:0.556430:0.200516:0.545160:0.200516:0.000000
mínimo de la función. Ejemplo:   = 3cos(2 ) + 1. La amplitud es 3.:@0.404235:0.234219:0.863730:0.234219:0.863730:0.217722:0.404235:0.217722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.626594:0.234335:0.634281:0.234335:0.634281:0.217866:0.626594:0.217866:0.000000
x:@0.698897:0.234335:0.706372:0.234335:0.706372:0.217866:0.698897:0.217866:0.000000
•:@0.404235:0.264352:0.411998:0.264352:0.411998:0.247160:0.404235:0.247160:0.000000
  Si   > 1 o si   < –1, la función sufre un proceso de dilatación.:@0.411998:0.263643:0.863148:0.263643:0.863148:0.247146:0.411998:0.247146:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.443921:0.263759:0.455191:0.263759:0.455191:0.247290:0.443921:0.247290:0.000000
A:@0.514798:0.263759:0.526068:0.263759:0.526068:0.247290:0.514798:0.247290:0.000000
•:@0.404235:0.281703:0.411998:0.281703:0.411998:0.264511:0.404235:0.264511:0.000000
  Si –1 <   < 1,  la función se contrae.:@0.411998:0.280994:0.682962:0.280994:0.682962:0.264497:0.411998:0.264497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.482008:0.281110:0.493279:0.281110:0.493279:0.264641:0.482008:0.264641:0.000000
Período (T):@0.404235:0.313888:0.492446:0.313888:0.492446:0.296942:0.404235:0.296942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Establece cuánto se requiere del dominio para que:@0.492450:0.313426:0.858007:0.313426:0.858007:0.296928:0.492450:0.296928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función describa un ciclo completo,   =        .:@0.404235:0.337905:0.739617:0.337905:0.739617:0.321407:0.404235:0.321407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.678970:0.338020:0.688776:0.338020:0.688776:0.321552:0.678970:0.321552:0.000000
Ejemplo:   = 3cos(2 ) + 1.    = π. Hasta π se completa un ciclo.:@0.404235:0.362384:0.849757:0.362384:0.849757:0.345886:0.404235:0.345886:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.469291:0.362499:0.476978:0.362499:0.476978:0.346031:0.469291:0.346031:0.000000
x:@0.542557:0.362499:0.550032:0.362499:0.550032:0.346031:0.542557:0.346031:0.000000
T:@0.594612:0.362499:0.604418:0.362499:0.604418:0.346031:0.594612:0.346031:0.000000
Frecuencia:@0.404235:0.395278:0.487037:0.395278:0.487037:0.378332:0.404235:0.378332:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Se relaciona con las veces que se repite el ciclo. Está de-:@0.487037:0.394815:0.891817:0.394815:0.891817:0.378317:0.487037:0.378317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
terminada por el valor de  .:@0.404235:0.412166:0.600199:0.412166:0.600199:0.395668:0.404235:0.395668:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
B:@0.588254:0.412282:0.597444:0.412282:0.597444:0.395813:0.588254:0.395813:0.000000
Ejemplo:   = 3cos(2 ) + 1. Como   es 2, el ciclo se repite 2 veces.:@0.404235:0.441590:0.857500:0.441590:0.857500:0.425092:0.404235:0.425092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.469291:0.441706:0.476978:0.441706:0.476978:0.425237:0.469291:0.425237:0.000000
x:@0.542557:0.441706:0.550032:0.441706:0.550032:0.425237:0.542557:0.425237:0.000000
B:@0.639614:0.441706:0.648803:0.441706:0.648803:0.425237:0.639614:0.425237:0.000000
Desplazamiento vertical :@0.404235:0.474484:0.597812:0.474484:0.597812:0.457538:0.404235:0.457538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Traslación vertical en   unidades.:@0.591030:0.474021:0.833981:0.474021:0.833981:0.457524:0.591030:0.457524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.750352:0.474137:0.761988:0.474137:0.761988:0.457668:0.750352:0.457668:0.000000
•:@0.404235:0.504154:0.411998:0.504154:0.411998:0.486962:0.404235:0.486962:0.000000
  Si   > 0, la gráfica se desplaza hacia arriba   unidades.:@0.411998:0.503445:0.809861:0.503445:0.809861:0.486948:0.411998:0.486948:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.443921:0.503561:0.455557:0.503561:0.455557:0.487092:0.443921:0.487092:0.000000
D:@0.726232:0.503561:0.737868:0.503561:0.737868:0.487092:0.726232:0.487092:0.000000
•:@0.404235:0.521505:0.411998:0.521505:0.411998:0.504313:0.404235:0.504313:0.000000
  Si   < 0, la gráfica se desplaza hacia abajo   unidades.:@0.411998:0.520796:0.808011:0.520796:0.808011:0.504298:0.411998:0.504298:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.443921:0.520912:0.455557:0.520912:0.455557:0.504443:0.443921:0.504443:0.000000
D:@0.724383:0.520912:0.736019:0.520912:0.736019:0.504443:0.724383:0.504443:0.000000
Desfase:@0.404235:0.557262:0.463013:0.557262:0.463013:0.540316:0.404235:0.540316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:        , desplazamiento horizontal de         unidades a:@0.463013:0.556799:0.831209:0.556799:0.831209:0.540301:0.463013:0.540301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la derecha o a la izquierda, según si   es negativo o positivo. :@0.404235:0.581278:0.829571:0.581278:0.829571:0.564780:0.404235:0.564780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
C:@0.654257:0.581394:0.664294:0.581394:0.664294:0.564925:0.654257:0.564925:0.000000
Ejemplo:   = 4sen    –       ; la gráfica de la función se desplaza π/2:@0.404235:0.613709:0.867691:0.613709:0.867691:0.597212:0.404235:0.597212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.469291:0.613825:0.476978:0.613825:0.476978:0.597356:0.469291:0.597356:0.000000
x:@0.536893:0.613825:0.544368:0.613825:0.544368:0.597356:0.536893:0.597356:0.000000
unidades a la derecha con relación al sen( ).:@0.404235:0.638188:0.714710:0.638188:0.714710:0.621691:0.404235:0.621691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.698527:0.638304:0.706002:0.638304:0.706002:0.621835:0.698527:0.621835:0.000000
Ejercicio resuelto:@0.404235:0.670996:0.522213:0.670996:0.522213:0.654209:0.404235:0.654209:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Grafiquemos la función  ( ) = –3sen  2  –       ,        .:@0.404235:0.687971:0.803551:0.687994:0.803551:0.671497:0.404235:0.671473:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.576023:0.688086:0.593747:0.688086:0.593747:0.671617:0.576023:0.671617:0.000000:0.000000:0.000000
x:@0.678610:0.688086:0.686085:0.688086:0.686085:0.671617:0.678610:0.671617:0.000000
∀:@0.744896:0.695581:0.756469:0.695581:0.756469:0.676582:0.744896:0.676582:0.000000
x:@0.756475:0.688110:0.763950:0.688110:0.763950:0.671641:0.756475:0.671641:0.000000
:@0.768092:0.687476:0.782744:0.687476:0.782744:0.674103:0.768092:0.674103:0.000000
R:@0.786887:0.687026:0.800796:0.687026:0.800796:0.673579:0.786887:0.673579:0.000000
Amplitud = | | = |–3| = 3.      Período =   =        =        = π.:@0.404240:0.727554:0.821102:0.727554:0.821102:0.711057:0.404240:0.711057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.497330:0.727670:0.508600:0.727670:0.508600:0.711201:0.497330:0.711201:0.000000
T:@0.691158:0.727670:0.700964:0.727670:0.700964:0.711201:0.691158:0.711201:0.000000
Desfase =         =                  =      . Vamos a graficar cada función.:@0.404240:0.767114:0.855891:0.767114:0.855891:0.750616:0.404240:0.750616:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2π:@0.712631:0.330419:0.731530:0.330419:0.731530:0.313922:0.712631:0.313922:0.000000:0.000000
B:@0.717486:0.346874:0.726675:0.346874:0.726675:0.330405:0.717486:0.330405:0.000000
–:@0.474931:0.550159:0.485431:0.550159:0.485431:0.533661:0.474931:0.533661:0.000000
C:@0.485431:0.550275:0.495468:0.550275:0.495468:0.533806:0.485431:0.533806:0.000000
B:@0.480595:0.566613:0.489785:0.566613:0.489785:0.550145:0.480595:0.550145:0.000000
–:@0.726217:0.550159:0.736717:0.550159:0.736717:0.533661:0.726217:0.533661:0.000000
C:@0.736717:0.550275:0.746754:0.550275:0.746754:0.533806:0.736717:0.533806:0.000000
B:@0.731881:0.566613:0.741071:0.566613:0.741071:0.550145:0.731881:0.550145:0.000000
π:@0.564684:0.606461:0.575087:0.606461:0.575087:0.589963:0.564684:0.589963:0.000000
2:@0.565628:0.622800:0.574124:0.622800:0.574124:0.606302:0.565628:0.606302:0.000000
π:@0.706228:0.680959:0.716632:0.680959:0.716632:0.664461:0.706228:0.664461:0.000000
3:@0.707172:0.697297:0.715668:0.697297:0.715668:0.680800:0.707172:0.680800:0.000000
2π:@0.722815:0.720024:0.741714:0.720024:0.741714:0.703527:0.722815:0.703527:0.000000:0.000000
B:@0.727670:0.736479:0.736859:0.736479:0.736859:0.720010:0.727670:0.720010:0.000000
2π:@0.766939:0.720024:0.785838:0.720024:0.785838:0.703527:0.766939:0.703527:0.000000:0.000000
2:@0.772353:0.736479:0.780425:0.736479:0.780425:0.720010:0.772353:0.720010:0.000000
–:@0.481698:0.759752:0.492197:0.759752:0.492197:0.743255:0.481698:0.743255:0.000000
C:@0.492197:0.759868:0.502234:0.759868:0.502234:0.743399:0.492197:0.743399:0.000000
B:@0.487362:0.776207:0.496551:0.776207:0.496551:0.759738:0.487362:0.759738:0.000000
2:@0.555103:0.776097:0.563599:0.776097:0.563599:0.759600:0.555103:0.759600:0.000000
π:@0.613423:0.759752:0.623827:0.759752:0.623827:0.743255:0.613423:0.743255:0.000000
6:@0.614367:0.776091:0.622863:0.776091:0.622863:0.759593:0.614367:0.759593:0.000000
π:@0.564597:0.744021:0.575000:0.744021:0.575000:0.727523:0.564597:0.727523:0.000000
3:@0.565541:0.760360:0.574037:0.760360:0.574037:0.743862:0.565541:0.743862:0.000000
– –:@0.531335:0.751293:0.561023:0.751293:0.561023:0.734796:0.531335:0.734796:0.000000:0.000000:0.000000
p:@0.386959:0.937776:0.398440:0.937776:0.398440:0.927751:0.386959:0.927751:0.000000
 :@0.398440:0.938484:0.401321:0.938484:0.401321:0.927007:0.398440:0.927007:0.000000
Figura 5.4.   = sen( ):@0.401321:0.938484:0.501608:0.938484:0.501608:0.927007:0.401321:0.927007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.452771:0.938564:0.458119:0.938564:0.458119:0.927108:0.452771:0.927108:0.000000
x:@0.492267:0.938564:0.497467:0.938564:0.497467:0.927108:0.492267:0.927108:0.000000
2:@0.309922:0.803535:0.315832:0.803535:0.315832:0.792058:0.309922:0.792058:0.000000
1:@0.309922:0.830260:0.315832:0.830260:0.315832:0.818783:0.309922:0.818783:0.000000
0:@0.313272:0.850699:0.319183:0.850699:0.319183:0.839222:0.313272:0.839222:0.000000
–1:@0.302618:0.883710:0.315832:0.883710:0.315832:0.872234:0.302618:0.872234:0.000000:0.000000
–2:@0.302618:0.910436:0.315832:0.910436:0.315832:0.898959:0.302618:0.898959:0.000000:0.000000
π:@0.379407:0.866180:0.386644:0.866180:0.386644:0.854703:0.379407:0.854703:0.000000
–π:@0.253684:0.866180:0.268225:0.866180:0.268225:0.854703:0.253684:0.854703:0.000000:0.000000
–2π:@0.194716:0.866180:0.215167:0.866180:0.215167:0.854703:0.194716:0.854703:0.000000:0.000000:0.000000
–3π:@0.145062:0.866180:0.165513:0.866180:0.165513:0.854703:0.145062:0.854703:0.000000:0.000000:0.000000
2π:@0.435803:0.866180:0.448950:0.866180:0.448950:0.854703:0.435803:0.854703:0.000000:0.000000
3π:@0.486784:0.866180:0.499931:0.866180:0.499931:0.854703:0.486784:0.854703:0.000000:0.000000
p:@0.771638:0.937776:0.783118:0.937776:0.783118:0.927751:0.771638:0.927751:0.000000
 :@0.783118:0.938484:0.786000:0.938484:0.786000:0.927007:0.783118:0.927007:0.000000
Figura 5.5.   = sen(2 ):@0.786000:0.938484:0.892197:0.938484:0.892197:0.927007:0.786000:0.927007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.837450:0.938564:0.842797:0.938564:0.842797:0.927108:0.837450:0.927108:0.000000
x:@0.882856:0.938564:0.888055:0.938564:0.888055:0.927108:0.882856:0.927108:0.000000
2:@0.699251:0.803535:0.705161:0.803535:0.705161:0.792058:0.699251:0.792058:0.000000
1:@0.699251:0.830260:0.705161:0.830260:0.705161:0.818783:0.699251:0.818783:0.000000
0:@0.702601:0.850699:0.708512:0.850699:0.708512:0.839222:0.702601:0.839222:0.000000
–1:@0.691947:0.883710:0.705161:0.883710:0.705161:0.872234:0.691947:0.872234:0.000000:0.000000
–2:@0.691947:0.910436:0.705161:0.910436:0.705161:0.898959:0.691947:0.898959:0.000000:0.000000
π:@0.768737:0.866180:0.775974:0.866180:0.775974:0.854703:0.768737:0.854703:0.000000
–π:@0.643013:0.866180:0.657554:0.866180:0.657554:0.854703:0.643013:0.854703:0.000000:0.000000
–2π:@0.584045:0.866180:0.604496:0.866180:0.604496:0.854703:0.584045:0.854703:0.000000:0.000000:0.000000
–3π:@0.534391:0.866180:0.554842:0.866180:0.554842:0.854703:0.534391:0.854703:0.000000:0.000000:0.000000
2π:@0.825132:0.866180:0.838279:0.866180:0.838279:0.854703:0.825132:0.854703:0.000000:0.000000
3π:@0.876113:0.866180:0.889260:0.866180:0.889260:0.854703:0.876113:0.854703:0.000000:0.000000
Competencia :@0.200596:0.103270:0.298219:0.103270:0.298219:0.087798:0.200596:0.087798:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.200596:0.115838:0.310971:0.115838:0.310971:0.100366:0.200596:0.100366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Alguna vez has notado :@0.200834:0.140313:0.358632:0.140313:0.358632:0.125250:0.200834:0.125250:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que algún compañero está :@0.154290:0.156155:0.330769:0.156155:0.330769:0.141092:0.154290:0.141092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
angustiado o preocupado, :@0.154290:0.171997:0.328059:0.171997:0.328059:0.156934:0.154290:0.156934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
como si llevara un gran peso en :@0.154290:0.187839:0.362957:0.187839:0.362957:0.172776:0.154290:0.172776:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
su espalda? :@0.154290:0.203681:0.230154:0.203681:0.230154:0.188618:0.154290:0.188618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Responde:@0.154290:0.227074:0.223243:0.227074:0.223243:0.211602:0.154290:0.211602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
: ¿serías capas de :@0.223243:0.226652:0.333619:0.226652:0.333619:0.211589:0.223243:0.211589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ayudarlo?, ¿por qué?:@0.154290:0.242494:0.284052:0.242494:0.284052:0.227431:0.154290:0.227431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.199644:0.305926:0.297267:0.305926:0.297267:0.290454:0.199644:0.290454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comunicacional:@0.199644:0.318494:0.311603:0.318494:0.311603:0.303021:0.199644:0.303021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Salud:@0.193071:0.343391:0.232173:0.343391:0.232173:0.327919:0.193071:0.327919:0.000000:0.000000:0.000000:0.000000:0.000000
Las funciones trigonométricas :@0.153335:0.358810:0.351819:0.358810:0.351819:0.343747:0.153335:0.343747:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son un grupo de funciones :@0.153335:0.374652:0.332099:0.374652:0.332099:0.359589:0.153335:0.359589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales muy importantes en ma-:@0.153335:0.390494:0.355919:0.390494:0.355919:0.375431:0.153335:0.375431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
temática. Estas tienen muchas :@0.153335:0.406336:0.352751:0.406336:0.352751:0.391273:0.153335:0.391273:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicaciones en física, química, :@0.153335:0.422178:0.353312:0.422178:0.353312:0.407115:0.153335:0.407115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
economía, en las distintas :@0.153335:0.438020:0.323114:0.438020:0.323114:0.422957:0.153335:0.422957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ramas de la ingeniería, entre :@0.153335:0.453862:0.336939:0.453862:0.336939:0.438799:0.153335:0.438799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
otras áreas.:@0.153335:0.469704:0.224609:0.469704:0.224609:0.454641:0.153335:0.454641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Por ejemplo, las funciones trigo-:@0.153335:0.492675:0.351061:0.492675:0.351061:0.477612:0.153335:0.477612:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
nométricas son muy utilizadas en :@0.153335:0.508517:0.364869:0.508517:0.364869:0.493454:0.153335:0.493454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la lectura de electrocardiogramas.:@0.153335:0.524359:0.361402:0.524359:0.361402:0.509296:0.153335:0.509296:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p :@0.153344:0.657410:0.176551:0.657410:0.176551:0.647386:0.153344:0.647386:0.000000:0.000000
Aplicaciones de las funciones  :@0.176551:0.658118:0.327172:0.658118:0.327172:0.646641:0.176551:0.646641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométricas en electrocardiogramas.:@0.153339:0.670188:0.352558:0.670188:0.352558:0.658711:0.153339:0.658711:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Indaga responde:@0.153344:0.698643:0.281202:0.698643:0.281202:0.683170:0.153344:0.683170:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 y :@0.200976:0.698220:0.215681:0.698220:0.215681:0.683157:0.200976:0.683157:0.000000:0.000000:0.000000
: ¿cuál es la :@0.281206:0.698220:0.354255:0.698220:0.354255:0.683157:0.281206:0.683157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función trigonométrica que se :@0.153344:0.714062:0.353921:0.714062:0.353921:0.698999:0.153344:0.698999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
relaciona con los catetos?:@0.153344:0.729904:0.317387:0.729904:0.317387:0.714841:0.153344:0.714841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Shutterstock,1791139382:@0.145516:0.639299:0.145516:0.569420:0.134047:0.569420:0.134047:0.639299:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000