178:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Funciones tangente y cotangente:@0.404235:0.127666:0.811368:0.127666:0.811368:0.083007:0.404235:0.083007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función tangente:@0.404236:0.163975:0.544814:0.163975:0.544814:0.146292:0.404236:0.146292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta función se denota con :@0.404236:0.179676:0.605516:0.179676:0.605516:0.163179:0.404236:0.163179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tan:@0.606518:0.179792:0.632468:0.179792:0.632468:0.163323:0.606518:0.163323:0.000000:0.000000:0.000000
 y el valor numérico en       en el :@0.632452:0.179676:0.895918:0.179676:0.895918:0.163179:0.632452:0.163179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.804376:0.179792:0.811850:0.179792:0.811850:0.163323:0.804376:0.163323:0.000000
:@0.816975:0.179460:0.833023:0.179460:0.833023:0.164813:0.816975:0.164813:0.000000
R:@0.838939:0.178590:0.852244:0.178590:0.852244:0.165727:0.838939:0.165727:0.000000
que está definida; se designa con tan( ) que, a su vez, se define como: :@0.404230:0.196015:0.895849:0.196015:0.895849:0.179517:0.404230:0.179517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.668078:0.196131:0.675552:0.196131:0.675552:0.179662:0.668078:0.179662:0.000000
 :@0.891707:0.196015:0.895849:0.196015:0.895849:0.179517:0.891707:0.179517:0.000000
tan( ) =              ,    cos( ) ≠ 0.:@0.543653:0.219482:0.752334:0.219482:0.752334:0.202984:0.543653:0.202984:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.573379:0.219598:0.580854:0.219598:0.580854:0.203129:0.573379:0.203129:0.000000
x:@0.708564:0.219598:0.716038:0.219598:0.716038:0.203129:0.708564:0.203129:0.000000
Para determinar el dominio de la función tangente, resolvemos la :@0.404230:0.252174:0.895916:0.252174:0.895916:0.235676:0.404230:0.235676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ecuación      , tal que cos( ) = 0, cuya solución es::@0.404230:0.268512:0.775115:0.268530:0.775115:0.252032:0.404230:0.252015:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.472699:0.268628:0.480174:0.268628:0.480174:0.252159:0.472699:0.252159:0.000000
:@0.484316:0.268295:0.500364:0.268295:0.500364:0.253649:0.484316:0.253649:0.000000
R:@0.505282:0.267443:0.518586:0.267443:0.518586:0.254581:0.505282:0.254581:0.000000
x:@0.608262:0.268646:0.615737:0.268646:0.615737:0.252177:0.608262:0.252177:0.000000
x:@0.573510:0.292113:0.580985:0.292113:0.580985:0.275644:0.573510:0.275644:0.000000
 =      +  π,         .:@0.580985:0.291997:0.722491:0.292002:0.722491:0.275505:0.580985:0.275499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
k:@0.635737:0.292113:0.643982:0.292113:0.643982:0.275644:0.635737:0.275644:0.000000
k:@0.673709:0.292113:0.681954:0.292113:0.681954:0.275644:0.673709:0.275644:0.000000
:@0.686481:0.291780:0.702529:0.291780:0.702529:0.277133:0.686481:0.277133:0.000000
Z:@0.707445:0.290916:0.719736:0.290916:0.719736:0.278053:0.707445:0.278053:0.000000
Por lo tanto, :@0.404229:0.315469:0.495700:0.315469:0.495700:0.298972:0.404229:0.298972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
{      | cos( ) = 0} =        +  π |     :@0.500805:0.331808:0.770545:0.331820:0.770545:0.315322:0.500805:0.315310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.506662:0.331924:0.514137:0.331924:0.514137:0.315455:0.506662:0.315455:0.000000
:@0.518279:0.331591:0.534327:0.331591:0.534327:0.316944:0.518279:0.316944:0.000000
R:@0.539254:0.330733:0.552559:0.330733:0.552559:0.317871:0.539254:0.317871:0.000000
x:@0.595347:0.331936:0.602822:0.331936:0.602822:0.315467:0.595347:0.315467:0.000000
k:@0.705255:0.331936:0.713501:0.331936:0.713501:0.315467:0.705255:0.315467:0.000000
k:@0.737197:0.331936:0.745442:0.331936:0.745442:0.315467:0.737197:0.315467:0.000000
:@0.749970:0.331603:0.766018:0.331603:0.766018:0.316956:0.749970:0.316956:0.000000
Z  :@0.770926:0.330733:0.792431:0.330733:0.792431:0.317871:0.770926:0.317871:0.000000:0.000000:0.000000
,:@0.792431:0.331820:0.795186:0.331820:0.795186:0.315322:0.792431:0.315322:0.000000
 :@0.404236:0.348159:0.408378:0.348159:0.408378:0.331661:0.404236:0.331661:0.000000
de donde :@0.404236:0.364497:0.477271:0.364497:0.477271:0.348000:0.404236:0.348000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom:@0.477271:0.364613:0.512486:0.364613:0.512486:0.348144:0.477271:0.348144:0.000000:0.000000:0.000000
(Tan) =   \        +  π |        .:@0.512488:0.364497:0.729285:0.364510:0.729285:0.348012:0.512488:0.348000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.569202:0.363423:0.582507:0.363423:0.582507:0.350561:0.569202:0.350561:0.000000
k:@0.640283:0.364625:0.648529:0.364625:0.648529:0.348157:0.640283:0.348157:0.000000
k:@0.672225:0.364625:0.680471:0.364625:0.680471:0.348157:0.672225:0.348157:0.000000
:@0.684998:0.364293:0.701046:0.364293:0.701046:0.349646:0.684998:0.349646:0.000000
Z:@0.705955:0.363423:0.718246:0.363423:0.718246:0.350561:0.705955:0.350561:0.000000
Mostremos que :@0.404242:0.397201:0.521356:0.397201:0.521356:0.380704:0.404242:0.380704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Rec:@0.521356:0.397317:0.545187:0.397317:0.545187:0.380848:0.521356:0.380848:0.000000:0.000000:0.000000
(Tan) =  . En efecto, sea      . Supongamos::@0.545187:0.397201:0.871396:0.397200:0.871396:0.380702:0.545187:0.380704:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.601894:0.396113:0.615199:0.396113:0.615199:0.383250:0.601894:0.383250:0.000000
y:@0.721753:0.397315:0.729440:0.397315:0.729440:0.380847:0.721753:0.380847:0.000000
:@0.733582:0.396983:0.749630:0.396983:0.749630:0.382336:0.733582:0.382336:0.000000
R:@0.754542:0.396113:0.767847:0.396113:0.767847:0.383250:0.754542:0.383250:0.000000
y:@0.487923:0.420782:0.495610:0.420782:0.495610:0.404313:0.487923:0.404313:0.000000
 = tan( ) =              ,   para algún   ≠      +  π.:@0.495610:0.420667:0.808092:0.420667:0.808092:0.404169:0.495610:0.404169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.544428:0.420782:0.551903:0.420782:0.551903:0.404313:0.544428:0.404313:0.000000
x:@0.724462:0.420782:0.731937:0.420782:0.731937:0.404313:0.724462:0.404313:0.000000
k:@0.786688:0.420782:0.794934:0.420782:0.794934:0.404313:0.786688:0.404313:0.000000
Entonces,   =               , y de la relación sen ( ) + cos ( ) = 1 :@0.404235:0.453358:0.829862:0.453362:0.829862:0.436864:0.404235:0.436861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.476381:0.453474:0.484068:0.453474:0.484068:0.437005:0.476381:0.437005:0.000000
2:@0.484070:0.447010:0.489023:0.447010:0.489023:0.437392:0.484070:0.437392:0.000000
2:@0.706831:0.447010:0.711785:0.447010:0.711785:0.437392:0.706831:0.437392:0.000000
x:@0.717738:0.453478:0.725213:0.453478:0.725213:0.437009:0.717738:0.437009:0.000000
2:@0.773799:0.447010:0.778752:0.447010:0.778752:0.437392:0.773799:0.437392:0.000000
x:@0.784704:0.453478:0.792179:0.453478:0.792179:0.437009:0.784704:0.437009:0.000000
 :@0.404235:0.469701:0.408377:0.469701:0.408377:0.453203:0.404235:0.453203:0.000000
se sigue que::@0.404235:0.486039:0.492699:0.486039:0.492699:0.469542:0.404235:0.469542:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.411864:0.509622:0.419550:0.509622:0.419550:0.493153:0.411864:0.493153:0.000000
2:@0.419545:0.503173:0.424498:0.503173:0.424498:0.493555:0.419545:0.493555:0.000000
cos ( ) = sen ( ) :@0.424498:0.509526:0.543982:0.509526:0.543982:0.493028:0.424498:0.493028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.448039:0.503173:0.452992:0.503173:0.452992:0.493555:0.448039:0.493555:0.000000
x:@0.458945:0.509641:0.466420:0.509641:0.466420:0.493173:0.458945:0.493173:0.000000
2:@0.515506:0.503173:0.520459:0.503173:0.520459:0.493555:0.515506:0.493555:0.000000
x:@0.526412:0.509641:0.533887:0.509641:0.533887:0.493173:0.526412:0.493173:0.000000
⇔:@0.543982:0.509020:0.564057:0.509020:0.564057:0.491307:0.543982:0.491307:0.000000
  (1 – sen ( )) = sen ( ) :@0.564057:0.509526:0.740007:0.509526:0.740007:0.493028:0.564057:0.493028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.568199:0.509641:0.575885:0.509641:0.575885:0.493173:0.568199:0.493173:0.000000
2:@0.575885:0.503173:0.580838:0.503173:0.580838:0.493555:0.575885:0.493555:0.000000
2:@0.638111:0.503173:0.643065:0.503173:0.643065:0.493555:0.638111:0.493555:0.000000
x:@0.649018:0.509641:0.656493:0.509641:0.656493:0.493173:0.649018:0.493173:0.000000
2:@0.711532:0.503173:0.716485:0.503173:0.716485:0.493555:0.711532:0.493555:0.000000
x:@0.722437:0.509641:0.729912:0.509641:0.729912:0.493173:0.722437:0.493173:0.000000
⇔:@0.740007:0.509020:0.760081:0.509020:0.760081:0.491307:0.740007:0.491307:0.000000
 sen ( ) =             .:@0.760081:0.509526:0.884150:0.509526:0.884150:0.493028:0.760081:0.493028:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.788266:0.503173:0.793220:0.503173:0.793220:0.493555:0.788266:0.493555:0.000000
x:@0.799171:0.509641:0.806646:0.509641:0.806646:0.493173:0.799171:0.493173:0.000000
Como 0 ≤              ≤ 1, la ecuación      , tal que sen( ) =               , :@0.404234:0.542217:0.880960:0.542215:0.880960:0.525718:0.404234:0.525720:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.649421:0.542333:0.656895:0.542333:0.656895:0.525864:0.649421:0.525864:0.000000
:@0.661038:0.542000:0.677085:0.542000:0.677085:0.527354:0.661038:0.527354:0.000000
R:@0.681998:0.541129:0.695302:0.541129:0.695302:0.528266:0.681998:0.528266:0.000000
x:@0.785481:0.542331:0.792956:0.542331:0.792956:0.525862:0.785481:0.525862:0.000000
tiene solución en  . Es decir, existe       \       +  π |        ,:@0.404243:0.578464:0.843153:0.578468:0.843153:0.561971:0.404243:0.561966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.530229:0.577382:0.543534:0.577382:0.543534:0.564519:0.530229:0.564519:0.000000
x:@0.654635:0.578584:0.662110:0.578584:0.662110:0.562115:0.654635:0.562115:0.000000
:@0.666252:0.578252:0.682300:0.578252:0.682300:0.563605:0.666252:0.563605:0.000000
R:@0.687211:0.577382:0.700516:0.577382:0.700516:0.564519:0.687211:0.564519:0.000000
k:@0.754150:0.578584:0.762396:0.578584:0.762396:0.562115:0.754150:0.562115:0.000000
k:@0.786092:0.578584:0.794338:0.578584:0.794338:0.562115:0.786092:0.562115:0.000000
:@0.798865:0.578252:0.814913:0.578252:0.814913:0.563605:0.798865:0.563605:0.000000
Z:@0.819823:0.577382:0.832114:0.577382:0.832114:0.564519:0.819823:0.564519:0.000000
tal que sen( ) =               .:@0.404233:0.611160:0.580778:0.611160:0.580778:0.594663:0.404233:0.594663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.487515:0.611276:0.494989:0.611276:0.494989:0.594807:0.487515:0.594807:0.000000
Nota que no estamos interesados en el valor numérico de la ecua-:@0.404233:0.641755:0.891757:0.641755:0.891757:0.625258:0.404233:0.625258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ción, sino en la existencia de soluciones.:@0.404233:0.658094:0.685504:0.658094:0.685504:0.641596:0.404233:0.641596:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La función tangente está definida como sigue::@0.404233:0.690786:0.730525:0.690786:0.730525:0.674288:0.404233:0.674288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Tan::@0.551574:0.727251:0.580144:0.727251:0.580144:0.710754:0.551574:0.710754:0.000000:0.000000:0.000000:0.000000
                                       :@0.580144:0.723477:0.741683:0.723477:0.741683:0.706980:0.580144:0.706980:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. ):@0.741683:0.729767:0.734284:0.730407:0.734284:0.713909:0.741683:0.713269:0.000000:0.000000:0.000000
La función tangente es periódica de período π, esto es,:@0.404233:0.763297:0.791786:0.763297:0.791786:0.746800:0.404233:0.746800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tan(  + π) = tan( ),          :@0.507957:0.786764:0.712451:0.786776:0.712451:0.770278:0.507957:0.770267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.537683:0.786880:0.545158:0.786880:0.545158:0.770411:0.537683:0.770411:0.000000
x:@0.629424:0.786880:0.636899:0.786880:0.636899:0.770411:0.629424:0.770411:0.000000
∀:@0.670459:0.794362:0.682031:0.794362:0.682031:0.775363:0.670459:0.775363:0.000000
x:@0.682040:0.786891:0.689514:0.786891:0.689514:0.770422:0.682040:0.770422:0.000000
:@0.693656:0.786257:0.708308:0.786257:0.708308:0.772884:0.693656:0.772884:0.000000
Dom:@0.712451:0.786891:0.747668:0.786891:0.747668:0.770422:0.712451:0.770422:0.000000:0.000000:0.000000
(Tan).:@0.747668:0.786776:0.788048:0.786776:0.788048:0.770278:0.747668:0.770278:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Además, esta función es impar, pues::@0.404245:0.819467:0.664746:0.819467:0.664746:0.802970:0.404245:0.802970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tan(– ) =                =                = –              = –tan( ),       :@0.404245:0.846506:0.816344:0.846501:0.816344:0.830003:0.404245:0.830008:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.444471:0.846621:0.451946:0.846621:0.451946:0.830152:0.444471:0.830152:0.000000
x:@0.746319:0.846621:0.753794:0.846621:0.753794:0.830152:0.746319:0.830152:0.000000
∀:@0.774524:0.854088:0.786097:0.854088:0.786097:0.835089:0.774524:0.835089:0.000000
x:@0.786105:0.846617:0.793580:0.846617:0.793580:0.830148:0.786105:0.830148:0.000000
:@0.797551:0.845983:0.812203:0.845983:0.812203:0.832609:0.797551:0.832609:0.000000
Dom:@0.816171:0.846617:0.851388:0.846617:0.851388:0.830148:0.816171:0.830148:0.000000:0.000000:0.000000
(Tan).:@0.851388:0.846501:0.891768:0.846501:0.891768:0.830003:0.851388:0.830003:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El grafo de Tan está definido como::@0.404241:0.879193:0.653549:0.879193:0.653549:0.862695:0.404241:0.862695:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G:@0.513706:0.895647:0.525150:0.895647:0.525150:0.879178:0.513706:0.879178:0.000000
(Tan) = {( , tan( )) | :@0.525150:0.895531:0.670449:0.895531:0.670449:0.879034:0.525150:0.879034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.593676:0.895647:0.601151:0.895647:0.601151:0.879178:0.593676:0.879178:0.000000
x:@0.637775:0.895647:0.645250:0.895647:0.645250:0.879178:0.637775:0.879178:0.000000
x  Dom:@0.670449:0.895647:0.736068:0.895652:0.736068:0.879183:0.670449:0.879178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.682058:0.895017:0.696710:0.895017:0.696710:0.881644:0.682058:0.881644:0.000000
 :@0.696710:0.895536:0.700852:0.895536:0.700852:0.879038:0.696710:0.879038:0.000000
(Tan)}.:@0.736068:0.895536:0.782305:0.895536:0.782305:0.879038:0.736068:0.879038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En la Figura 5.10., se muestra la gráfica de la función tangente. :@0.404244:0.919003:0.842580:0.919003:0.842580:0.902505:0.404244:0.902505:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen( ):@0.609076:0.215233:0.652500:0.215233:0.652500:0.198735:0.609076:0.198735:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.639072:0.215349:0.646547:0.215349:0.646547:0.198880:0.639072:0.198880:0.000000
cos( ):@0.609327:0.231572:0.652250:0.231572:0.652250:0.215074:0.609327:0.215074:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.638822:0.231687:0.646297:0.231687:0.646297:0.215218:0.638822:0.215218:0.000000
π:@0.604796:0.285087:0.615199:0.285087:0.615199:0.268590:0.604796:0.268590:0.000000
2:@0.605740:0.301426:0.614236:0.301426:0.614236:0.284928:0.605740:0.284928:0.000000
π:@0.608979:0.358040:0.619382:0.358040:0.619382:0.341542:0.608979:0.341542:0.000000
2:@0.609923:0.374378:0.618419:0.374378:0.618419:0.357881:0.609923:0.357881:0.000000
π:@0.674075:0.324912:0.684479:0.324912:0.684479:0.308415:0.674075:0.308415:0.000000
2:@0.675019:0.341251:0.683515:0.341251:0.683515:0.324753:0.675019:0.324753:0.000000
π:@0.755767:0.413495:0.766170:0.413495:0.766170:0.396998:0.755767:0.396998:0.000000
2:@0.756711:0.429834:0.765207:0.429834:0.765207:0.413336:0.756711:0.413336:0.000000
sen( ):@0.581361:0.413495:0.624785:0.413495:0.624785:0.396998:0.581361:0.396998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.611357:0.413611:0.618832:0.413611:0.618832:0.397142:0.611357:0.397142:0.000000
cos( ):@0.581611:0.429834:0.624534:0.429834:0.624534:0.413336:0.581611:0.413336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.611107:0.429950:0.618581:0.429950:0.618581:0.413481:0.611107:0.413481:0.000000
sen ( ):@0.510319:0.446928:0.558695:0.446928:0.558695:0.430431:0.510319:0.430431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.534362:0.440575:0.539315:0.440575:0.539315:0.430957:0.534362:0.430957:0.000000
x:@0.545267:0.447044:0.552742:0.447044:0.552742:0.430575:0.545267:0.430575:0.000000
cos ( ):@0.510570:0.463267:0.558445:0.463273:0.558445:0.446776:0.510570:0.446769:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.534111:0.456920:0.539064:0.456920:0.539064:0.447302:0.534111:0.447302:0.000000
x:@0.545017:0.463389:0.552492:0.463389:0.552492:0.446920:0.545017:0.446920:0.000000
y:@0.849636:0.502716:0.857322:0.502716:0.857322:0.486247:0.849636:0.486247:0.000000
2:@0.857322:0.496247:0.862275:0.496247:0.862275:0.486629:0.857322:0.486629:0.000000
1 + :@0.835842:0.518945:0.863429:0.518945:0.863429:0.502448:0.835842:0.502448:0.000000:0.000000:0.000000:0.000000
y:@0.863429:0.519061:0.871116:0.519061:0.871116:0.502592:0.863429:0.502592:0.000000
2:@0.871115:0.512592:0.876069:0.512592:0.876069:0.502974:0.871115:0.502974:0.000000
y:@0.499403:0.534736:0.507225:0.534736:0.507225:0.518238:0.499403:0.518238:0.000000
2:@0.507225:0.528383:0.512178:0.528383:0.512178:0.518765:0.507225:0.518765:0.000000
1 + :@0.485676:0.551081:0.513264:0.551081:0.513264:0.534583:0.485676:0.534583:0.000000:0.000000:0.000000:0.000000
y:@0.513264:0.551196:0.520951:0.551196:0.520951:0.534728:0.513264:0.534728:0.000000
2:@0.520950:0.544728:0.525903:0.544728:0.525903:0.535110:0.520950:0.535110:0.000000
y:@0.841454:0.534851:0.849140:0.534851:0.849140:0.518383:0.841454:0.518383:0.000000
  1 + :@0.821032:0.551074:0.856904:0.552332:0.856904:0.535835:0.821032:0.534577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.856904:0.552448:0.864591:0.552448:0.864591:0.535979:0.856904:0.535979:0.000000
2:@0.864599:0.545985:0.869552:0.545985:0.869552:0.536367:0.864599:0.536367:0.000000
π:@0.724438:0.572702:0.734841:0.572702:0.734841:0.556205:0.724438:0.556205:0.000000
2:@0.725382:0.589041:0.733878:0.589041:0.733878:0.572543:0.725382:0.572543:0.000000
y:@0.544517:0.604669:0.552204:0.604669:0.552204:0.588201:0.544517:0.588201:0.000000
  1 + :@0.524096:0.620892:0.559968:0.622150:0.559968:0.605653:0.524096:0.604395:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.559968:0.622266:0.567655:0.622266:0.567655:0.605797:0.559968:0.605797:0.000000
2:@0.567663:0.615804:0.572616:0.615804:0.572616:0.606186:0.567663:0.606186:0.000000
Dom:@0.592692:0.716992:0.627909:0.716992:0.627909:0.700523:0.592692:0.700523:0.000000:0.000000:0.000000
(Tan)    ,:@0.627909:0.716876:0.706018:0.716876:0.706018:0.700378:0.627909:0.700378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.669676:0.724975:0.685821:0.724975:0.685821:0.705112:0.669676:0.705112:0.000000
R:@0.689960:0.715789:0.703265:0.715789:0.703265:0.702927:0.689960:0.702927:0.000000
x:@0.592700:0.737899:0.600175:0.737899:0.600175:0.721431:0.592700:0.721431:0.000000
   tan( ) = :@0.600175:0.737784:0.686849:0.737784:0.686849:0.721286:0.600175:0.721286:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.604317:0.745882:0.620461:0.745882:0.620461:0.726020:0.604317:0.726020:0.000000
x:@0.654329:0.737899:0.661804:0.737899:0.661804:0.721431:0.654329:0.721431:0.000000
sen(:@0.690860:0.730407:0.720856:0.730407:0.720856:0.713909:0.690860:0.713909:0.000000:0.000000:0.000000:0.000000
x:@0.720856:0.730523:0.728331:0.730523:0.728331:0.714054:0.720856:0.714054:0.000000
cos( ):@0.691110:0.746746:0.734033:0.746746:0.734033:0.730248:0.691110:0.730248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.720605:0.746861:0.728080:0.746861:0.728080:0.730393:0.720605:0.730393:0.000000
sen( ):@0.642911:0.839814:0.686335:0.839814:0.686335:0.823316:0.642911:0.823316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.672907:0.839929:0.680382:0.839929:0.680382:0.823460:0.672907:0.823460:0.000000
cos( ):@0.643161:0.856152:0.686084:0.856152:0.686084:0.839655:0.643161:0.839655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.672656:0.856268:0.680131:0.856268:0.680131:0.839799:0.672656:0.839799:0.000000
–sen( ):@0.552714:0.839814:0.606792:0.839814:0.606792:0.823316:0.552714:0.823316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.593364:0.839929:0.600839:0.839929:0.600839:0.823460:0.593364:0.823460:0.000000
cos( ):@0.558301:0.856152:0.601224:0.856152:0.601224:0.839655:0.558301:0.839655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.587796:0.856268:0.595271:0.856268:0.595271:0.839799:0.587796:0.839799:0.000000
sen(– ):@0.477642:0.839814:0.531565:0.839814:0.531565:0.823316:0.477642:0.823316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.518137:0.839929:0.525612:0.839929:0.525612:0.823460:0.518137:0.823460:0.000000
cos(– ):@0.477892:0.856152:0.531315:0.856152:0.531315:0.839655:0.477892:0.839655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.517887:0.856268:0.525362:0.856268:0.525362:0.839799:0.517887:0.839799:0.000000
Saberes previos:@0.199646:0.111933:0.307805:0.111933:0.307805:0.096461:0.199646:0.096461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cómo se define la :@0.199884:0.140561:0.326090:0.140561:0.326090:0.125497:0.199884:0.125497:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función tangente?:@0.153341:0.156403:0.270418:0.156403:0.270418:0.141339:0.153341:0.141339:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.206791:0.363493:0.206791:0.363493:0.191319:0.199646:0.191319:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Cuál es el recorrido de :@0.199884:0.235419:0.353058:0.235419:0.353058:0.220356:0.199884:0.220356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función tangente?:@0.153341:0.251261:0.284842:0.251261:0.284842:0.236198:0.153341:0.236198:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.302154:0.893683:0.313634:0.893683:0.313634:0.883659:0.302154:0.883659:0.000000
 :@0.313634:0.894391:0.316516:0.894391:0.316516:0.882914:0.313634:0.882914:0.000000
Figura 5.10.:@0.316516:0.894391:0.370994:0.894391:0.370994:0.882914:0.316516:0.882914:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.362203:0.833702:0.366753:0.833702:0.366753:0.823678:0.362203:0.823678:0.000000
y:@0.244303:0.767641:0.248982:0.767641:0.248982:0.757617:0.244303:0.757617:0.000000
y:@0.269029:0.803308:0.273257:0.803308:0.273257:0.794250:0.269029:0.794250:0.000000
 = tan( ):@0.273257:0.803244:0.305797:0.803244:0.305797:0.794171:0.273257:0.794171:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.298412:0.803308:0.302523:0.803308:0.302523:0.794250:0.298412:0.794250:0.000000
π:@0.291263:0.830145:0.295944:0.830145:0.295944:0.822721:0.291263:0.822721:0.000000
0:@0.255359:0.828627:0.259053:0.828627:0.259053:0.821454:0.255359:0.821454:0.000000
3π:@0.308744:0.830145:0.317249:0.830145:0.317249:0.822721:0.308744:0.822721:0.000000:0.000000
2:@0.311102:0.836430:0.314925:0.836430:0.314925:0.829006:0.311102:0.829006:0.000000
5π:@0.347621:0.830145:0.356126:0.830145:0.356126:0.822721:0.347621:0.822721:0.000000:0.000000
2:@0.349980:0.836430:0.353803:0.836430:0.353803:0.829006:0.349980:0.829006:0.000000
2π:@0.328011:0.830145:0.336516:0.830145:0.336516:0.822721:0.328011:0.822721:0.000000:0.000000
π:@0.231772:0.830145:0.236453:0.830145:0.236453:0.822721:0.231772:0.822721:0.000000
2:@0.232197:0.836430:0.236020:0.836430:0.236020:0.829006:0.232197:0.829006:0.000000
π:@0.271793:0.830145:0.276475:0.830145:0.276475:0.822721:0.271793:0.822721:0.000000
2:@0.272218:0.836430:0.276041:0.836430:0.276041:0.829006:0.272218:0.829006:0.000000
3π:@0.190735:0.830145:0.199240:0.830145:0.199240:0.822721:0.190735:0.822721:0.000000:0.000000
2:@0.193076:0.836430:0.196899:0.836430:0.196899:0.829006:0.193076:0.829006:0.000000
5π:@0.151045:0.830145:0.159550:0.830145:0.159550:0.822721:0.151045:0.822721:0.000000:0.000000
2:@0.153386:0.836430:0.157209:0.836430:0.157209:0.829006:0.153386:0.829006:0.000000
–π:@0.209910:0.830145:0.219317:0.830145:0.219317:0.822721:0.209910:0.822721:0.000000:0.000000
–2π:@0.168662:0.830145:0.181891:0.830145:0.181891:0.822721:0.168662:0.822721:0.000000:0.000000:0.000000
–:@0.225689:0.832962:0.230413:0.832962:0.230413:0.825538:0.225689:0.825538:0.000000
–:@0.185497:0.832962:0.190222:0.832962:0.190222:0.825538:0.185497:0.825538:0.000000
–:@0.145809:0.832962:0.150534:0.832962:0.150534:0.825538:0.145809:0.825538:0.000000
M.5.1.72. Reconocer las funciones trigonométricas, tangente, cotangente, sus propiedades y las relaciones existentes entre estas funciones, y representarlas de manera gráfica :@0.145063:0.940354:0.895582:0.940354:0.895582:0.930312:0.145063:0.930312:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.892991:0.940354:0.895512:0.940354:0.895512:0.930312:0.892991:0.930312:0.000000
con apoyo de las TIC (calculadora gráfica, software, applets).:@0.145063:0.949155:0.391686:0.949155:0.391686:0.939113:0.145063:0.939113:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Algunas identidades :@0.200150:0.402246:0.334747:0.402246:0.334747:0.387183:0.200150:0.387183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
trigonométricas fundamentales :@0.153343:0.418088:0.360130:0.418088:0.360130:0.403025:0.153343:0.403025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
son::@0.153343:0.433930:0.179218:0.433930:0.179218:0.418867:0.153343:0.418867:0.000000:0.000000:0.000000:0.000000
•:@0.153343:0.457548:0.160432:0.457548:0.160432:0.441851:0.153343:0.441851:0.000000
  tan( ) =              ,  siempre que:@0.160432:0.456901:0.361500:0.456901:0.361500:0.441838:0.160432:0.441838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.197107:0.457007:0.203932:0.457007:0.203932:0.441970:0.197107:0.441970:0.000000
  cos( ) ≠ 0.:@0.153343:0.479872:0.236544:0.479872:0.236544:0.464809:0.153343:0.464809:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.196755:0.479978:0.203580:0.479978:0.203580:0.464941:0.196755:0.464941:0.000000
•:@0.153343:0.503490:0.160432:0.503490:0.160432:0.487793:0.153343:0.487793:0.000000
  cot( ) =              ,  siempre que:@0.160432:0.502843:0.361516:0.502843:0.361516:0.487780:0.160432:0.487780:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.196808:0.502949:0.203633:0.502949:0.203633:0.487912:0.196808:0.487912:0.000000
  sen( ) ≠ 0.:@0.153343:0.525814:0.237001:0.525814:0.237001:0.510751:0.153343:0.510751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.197213:0.525920:0.204037:0.525920:0.204037:0.510883:0.197213:0.510883:0.000000
•:@0.153343:0.549432:0.160432:0.549432:0.160432:0.533735:0.153343:0.533735:0.000000
  sen ( ) + cos ( ) = 1.:@0.160432:0.548785:0.302982:0.548781:0.302982:0.533718:0.160432:0.533722:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.191916:0.542981:0.196439:0.542981:0.196439:0.534199:0.191916:0.534199:0.000000
x:@0.201873:0.548887:0.208698:0.548887:0.208698:0.533850:0.201873:0.533850:0.000000
2:@0.253059:0.542981:0.257582:0.542981:0.257582:0.534199:0.253059:0.534199:0.000000
x:@0.263018:0.548887:0.269843:0.548887:0.269843:0.533850:0.263018:0.533850:0.000000
  1 + tan ( ) = sec ( ), cos( ) ≠ 0.:@0.153344:0.571752:0.361479:0.571751:0.361479:0.556688:0.153344:0.556689:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.214110:0.565951:0.218632:0.565951:0.218632:0.557170:0.214110:0.557170:0.000000
x:@0.223761:0.571856:0.230586:0.571856:0.230586:0.556820:0.223761:0.556820:0.000000
2:@0.271195:0.565951:0.275718:0.565951:0.275718:0.557170:0.271195:0.557170:0.000000
x:@0.280846:0.571856:0.287671:0.571856:0.287671:0.556820:0.280846:0.556820:0.000000
x:@0.324083:0.571856:0.330908:0.571856:0.330908:0.556820:0.324083:0.556820:0.000000
  1 + cot ( ) = csc ( ), sen( ) ≠ 0.:@0.153336:0.594722:0.361492:0.594720:0.361492:0.579657:0.153336:0.579659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.213854:0.588921:0.218376:0.588921:0.218376:0.580139:0.213854:0.580139:0.000000
x:@0.223479:0.594826:0.230304:0.594826:0.230304:0.579789:0.223479:0.579789:0.000000
2:@0.270761:0.588921:0.275284:0.588921:0.275284:0.580139:0.270761:0.580139:0.000000
x:@0.280385:0.594826:0.287210:0.594826:0.287210:0.579789:0.280385:0.579789:0.000000
x:@0.324024:0.594826:0.330849:0.594826:0.330849:0.579789:0.324024:0.579789:0.000000
sen( ):@0.229448:0.450033:0.269094:0.450033:0.269094:0.434970:0.229448:0.434970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.256835:0.450138:0.263659:0.450138:0.263659:0.435102:0.256835:0.435102:0.000000
cos( ):@0.229677:0.464950:0.268866:0.464950:0.268866:0.449887:0.229677:0.449887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.256606:0.465055:0.263431:0.465055:0.263431:0.450019:0.256606:0.450019:0.000000
cos( ):@0.229678:0.495952:0.268867:0.495952:0.268867:0.480889:0.229678:0.480889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.256607:0.496057:0.263431:0.496057:0.263431:0.481021:0.256607:0.481021:0.000000
sen( ):@0.229449:0.510869:0.269095:0.510869:0.269095:0.495806:0.229449:0.495806:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.256836:0.510974:0.263660:0.510974:0.263660:0.495938:0.256836:0.495938:0.000000
Competencia :@0.199912:0.364539:0.297535:0.364539:0.297535:0.349066:0.199912:0.349066:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.199912:0.377107:0.283975:0.377107:0.283975:0.361634:0.199912:0.361634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000