Funciones trigonométricas:@0.073089:0.043661:0.311884:0.043661:0.311884:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
44:@0.037229:0.974518:0.056728:0.974518:0.056728:0.957377:0.037229:0.957377:0.000000:0.000000
En este capítulo, definiremos las funciones trigonométricas: seno, coseno, tangente, :@0.293660:0.241789:0.931114:0.241789:0.931114:0.226077:0.293660:0.226077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cotangente, secante y cosecante. Observaremos, además, algunas propiedades, por :@0.293660:0.258431:0.931335:0.258431:0.931335:0.242719:0.293660:0.242719:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ejemplo, la periodicidad, y se construirán se construirán sus gráficas. :@0.293660:0.275073:0.788431:0.275073:0.788431:0.259360:0.293660:0.259360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.1 Funciones periódicas:@0.293660:0.303503:0.487137:0.303503:0.487137:0.286556:0.293660:0.286556:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Iniciamos el estudio con una clase de funciones denominadas :@0.293660:0.331933:0.735786:0.331933:0.735786:0.316220:0.293660:0.316220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
periódicas:@0.734992:0.331933:0.812631:0.331933:0.812631:0.315263:0.734992:0.315263:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
, cuya definición :@0.812413:0.331933:0.930963:0.331933:0.930963:0.316220:0.812413:0.316220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
se da a continuación.:@0.293679:0.348575:0.447140:0.348575:0.447140:0.332862:0.293679:0.332862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición:@0.293679:0.377004:0.371646:0.377004:0.371646:0.360335:0.293679:0.360335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean     0 y   una función real definida en todo  . Se dice que   es periódica :@0.371541:0.377004:0.931041:0.377004:0.931041:0.361292:0.371541:0.361292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.417375:0.377004:0.425493:0.377004:0.425493:0.361569:0.417375:0.361569:0.000000
.:@0.429045:0.376450:0.444379:0.376450:0.444379:0.362734:0.429045:0.362734:0.000000
f:@0.472082:0.377004:0.476775:0.377004:0.476775:0.361569:0.472082:0.361569:0.000000
R:@0.724059:0.376145:0.737349:0.376145:0.737349:0.363247:0.724059:0.363247:0.000000
f:@0.831373:0.377004:0.836067:0.377004:0.836067:0.361569:0.831373:0.361569:0.000000
de período 2  si y solo si   verifica la siguiente condición::@0.293679:0.393646:0.700422:0.393646:0.700422:0.377934:0.293679:0.377934:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.386782:0.393646:0.394900:0.393646:0.394900:0.378211:0.386782:0.378211:0.000000
f:@0.473738:0.393646:0.478432:0.393646:0.478432:0.378211:0.473738:0.378211:0.000000
f x:@0.518045:0.422076:0.534924:0.422076:0.534924:0.406641:0.518045:0.406641:0.000000:0.000000:0.000000
(    2 )    ( ),    :@0.522665:0.422076:0.643527:0.422076:0.643527:0.406363:0.522665:0.406363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1:@0.538808:0.421521:0.554141:0.421521:0.554141:0.407806:0.538808:0.407806:0.000000
T:@0.566897:0.422076:0.575015:0.422076:0.575015:0.406641:0.566897:0.406641:0.000000
5:@0.583685:0.421521:0.599018:0.421521:0.599018:0.407806:0.583685:0.407806:0.000000
f x:@0.602884:0.422076:0.619763:0.422076:0.619763:0.406641:0.602884:0.406641:0.000000:0.000000:0.000000
;:@0.643416:0.421521:0.655694:0.421521:0.655694:0.407806:0.643416:0.407806:0.000000
x:@0.655602:0.422076:0.663057:0.422076:0.663057:0.406641:0.655602:0.406641:0.000000
    .:@0.662983:0.422076:0.702540:0.422076:0.702540:0.406363:0.662983:0.406363:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.666941:0.421937:0.682274:0.421937:0.682274:0.407889:0.666941:0.407889:0.000000
R:@0.686140:0.421216:0.699430:0.421216:0.699430:0.408319:0.686140:0.408319:0.000000
En la Figura 5.1. se representa una función periódica de período 2 .:@0.293660:0.450506:0.777237:0.450506:0.777237:0.434793:0.293660:0.434793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.765990:0.450506:0.774108:0.450506:0.774108:0.435070:0.765990:0.435070:0.000000
Figura 5.1.:@0.800547:0.544981:0.854203:0.544981:0.854203:0.533554:0.800547:0.533554:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.541017:0.476243:0.547471:0.476243:0.547471:0.462912:0.541017:0.462912:0.000000
x:@0.838532:0.525412:0.844970:0.525412:0.844970:0.512081:0.838532:0.512081:0.000000
0:@0.544066:0.522237:0.550599:0.522237:0.550599:0.510810:0.544066:0.510810:0.000000
2:@0.490397:0.525535:0.501548:0.525535:0.501548:0.515560:0.490397:0.515560:0.000000
T:@0.501548:0.525939:0.507452:0.525939:0.507452:0.514713:0.501548:0.514713:0.000000
2:@0.432578:0.525535:0.443729:0.525535:0.443729:0.515560:0.432578:0.515560:0.000000
2:@0.443729:0.525939:0.450262:0.525939:0.450262:0.514511:0.443729:0.514511:0.000000
T:@0.450262:0.525939:0.456166:0.525939:0.456166:0.514713:0.450262:0.514713:0.000000
2:@0.378026:0.525535:0.389177:0.525535:0.389177:0.515560:0.378026:0.515560:0.000000
3:@0.389177:0.525939:0.395710:0.525939:0.395710:0.514511:0.389177:0.514511:0.000000
T:@0.395710:0.525939:0.401614:0.525939:0.401614:0.514713:0.395710:0.514713:0.000000
T:@0.605071:0.525939:0.610974:0.525939:0.610974:0.514713:0.605071:0.514713:0.000000
2:@0.656357:0.525939:0.662890:0.525939:0.662890:0.514511:0.656357:0.514511:0.000000
T:@0.662890:0.525939:0.668793:0.525939:0.668793:0.514713:0.662890:0.514713:0.000000
3:@0.710909:0.525939:0.717442:0.525939:0.717442:0.514511:0.710909:0.514511:0.000000
T:@0.717442:0.525939:0.723346:0.525939:0.723346:0.514713:0.717442:0.514713:0.000000
4:@0.765461:0.525939:0.771994:0.525939:0.771994:0.514511:0.765461:0.514511:0.000000
T:@0.771994:0.525939:0.777898:0.525939:0.777898:0.514713:0.771994:0.514713:0.000000
5:@0.820014:0.525939:0.826547:0.525939:0.826547:0.514511:0.820014:0.514511:0.000000
T:@0.826547:0.525939:0.832450:0.525939:0.832450:0.514713:0.826547:0.514713:0.000000
y:@0.638358:0.481515:0.645152:0.481515:0.645152:0.467483:0.638358:0.467483:0.000000
    ( ):@0.645152:0.481515:0.686334:0.481515:0.686334:0.467231:0.645152:0.467231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.648816:0.481011:0.662756:0.481011:0.662756:0.468542:0.648816:0.468542:0.000000
f x:@0.666420:0.481515:0.681899:0.481515:0.681899:0.467483:0.666420:0.467483:0.000000:0.000000:0.000000
La característica fundamental de las funciones periódicas es que basta conocer la función :@0.293660:0.574665:0.931252:0.574665:0.931252:0.558953:0.293660:0.558953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en un intervalo de longitud 2 , por ejemplo :@0.293660:0.591307:0.618217:0.591307:0.618217:0.575594:0.293660:0.575594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.508399:0.591307:0.516517:0.591307:0.516517:0.575872:0.508399:0.575872:0.000000
F:@0.618548:0.591890:0.622635:0.591890:0.622635:0.574235:0.618548:0.574235:0.000000
2:@0.622598:0.590752:0.637931:0.590752:0.637931:0.577037:0.622598:0.577037:0.000000
T T:@0.637894:0.591307:0.661658:0.591307:0.661658:0.575872:0.637894:0.575872:0.000000:0.000000:0.000000
,  , y luego reproducir esta porción de :@0.645975:0.591307:0.931022:0.591307:0.931022:0.575594:0.645975:0.575594:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G:@0.661621:0.591890:0.665708:0.591890:0.665708:0.574235:0.661621:0.574235:0.000000
función del lado positivo de los números reales a intervalos de la formas  , 3 ,  3 , 5 , :@0.293679:0.607949:0.930956:0.607949:0.930956:0.592236:0.293679:0.592236:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.825795:0.608531:0.829882:0.608531:0.829882:0.590877:0.825795:0.590877:0.000000
T T:@0.829827:0.607949:0.862518:0.607949:0.862518:0.592514:0.829827:0.592514:0.000000:0.000000:0.000000
G F:@0.862481:0.608531:0.878146:0.608531:0.878146:0.590877:0.862481:0.590877:0.000000:0.000000:0.000000
T T:@0.887036:0.607949:0.919728:0.607949:0.919728:0.592514:0.887036:0.592514:0.000000:0.000000:0.000000
G:@0.919691:0.608531:0.923777:0.608531:0.923777:0.590877:0.919691:0.590877:0.000000
F:@0.293679:0.625173:0.297765:0.625173:0.297765:0.607519:0.293679:0.607519:0.000000
5 , 7  y así sucesivamente; a continuación, del lado negativo a intervalos de la formas :@0.297710:0.624591:0.931409:0.624591:0.931409:0.608878:0.297710:0.608878:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T T:@0.306656:0.624591:0.339347:0.624591:0.339347:0.609155:0.306656:0.609155:0.000000:0.000000:0.000000
G:@0.339310:0.625173:0.343397:0.625173:0.343397:0.607519:0.339310:0.607519:0.000000
F:@0.293679:0.641815:0.297765:0.641815:0.297765:0.624161:0.293679:0.624161:0.000000
2:@0.297967:0.640678:0.313301:0.640678:0.313301:0.626962:0.297967:0.626962:0.000000
3 , :@0.313503:0.641233:0.338353:0.641233:0.338353:0.625520:0.313503:0.625520:0.000000:0.000000:0.000000:0.000000
T:@0.322670:0.641233:0.330788:0.641233:0.330788:0.625797:0.322670:0.625797:0.000000
2:@0.339862:0.640678:0.355196:0.640678:0.355196:0.626962:0.339862:0.626962:0.000000
T:@0.355398:0.641233:0.363516:0.641233:0.363516:0.625797:0.355398:0.625797:0.000000
G F:@0.363663:0.641815:0.380966:0.641815:0.380966:0.624161:0.363663:0.624161:0.000000:0.000000:0.000000
, :@0.367952:0.641233:0.375370:0.641233:0.375370:0.625520:0.367952:0.625520:0.000000:0.000000
2:@0.381168:0.640678:0.396501:0.640678:0.396501:0.626962:0.381168:0.626962:0.000000
5 ,  3 , y así sucesivamente. La gráfica de la función periódica en el :@0.396704:0.641233:0.930827:0.641233:0.930827:0.625520:0.396704:0.625520:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.405871:0.641233:0.413988:0.641233:0.413988:0.625797:0.405871:0.625797:0.000000
2:@0.423063:0.640678:0.438396:0.640678:0.438396:0.626962:0.423063:0.626962:0.000000
T:@0.447766:0.641233:0.455883:0.641233:0.455883:0.625797:0.447766:0.625797:0.000000
G:@0.456031:0.641815:0.460117:0.641815:0.460117:0.624161:0.456031:0.624161:0.000000
intervalo  – ,   se reproduce sucesivamente a cada uno de los intervalos de los tipos :@0.293586:0.657874:0.930757:0.657874:0.930757:0.642162:0.293586:0.642162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.363424:0.658457:0.367510:0.658457:0.367510:0.640803:0.363424:0.640803:0.000000
T T:@0.376824:0.657874:0.401122:0.657874:0.401122:0.642439:0.376824:0.642439:0.000000:0.000000:0.000000
G:@0.401158:0.658457:0.405245:0.658457:0.405245:0.640803:0.401158:0.640803:0.000000
antes indicados. Las funciones trigonométricas son funciones periódicas. :@0.293531:0.674516:0.823524:0.674516:0.823524:0.658804:0.293531:0.658804:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2.2 Función seno, gráfica y características:@0.293531:0.702946:0.615879:0.702946:0.615879:0.685999:0.293531:0.685999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta función se designa con :@0.293531:0.731376:0.498765:0.731376:0.498765:0.715663:0.293531:0.715663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen:@0.498496:0.731376:0.523924:0.731376:0.523924:0.715941:0.498496:0.715941:0.000000:0.000000:0.000000
 y se define como sigue::@0.523861:0.731376:0.698123:0.731376:0.698123:0.715663:0.523861:0.715663:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen:@0.523125:0.760513:0.548553:0.760513:0.548553:0.745078:0.523125:0.745078:0.000000:0.000000:0.000000
: :@0.548490:0.760513:0.555651:0.760513:0.555651:0.744800:0.548490:0.744800:0.000000:0.000000
5:@0.558189:0.766825:0.563761:0.766825:0.563761:0.742752:0.558189:0.742752:0.000000
R:@0.572769:0.755873:0.586059:0.755873:0.586059:0.742976:0.572769:0.742976:0.000000
R:@0.659113:0.755873:0.672403:0.755873:0.672403:0.742976:0.659113:0.742976:0.000000
x:@0.575691:0.769284:0.583146:0.769284:0.583146:0.753849:0.575691:0.753849:0.000000
Sen x:@0.644370:0.769279:0.682271:0.769279:0.682271:0.753844:0.644370:0.753844:0.000000:0.000000:0.000000:0.000000:0.000000
( ):@0.669938:0.769279:0.687149:0.769279:0.687149:0.753566:0.669938:0.753566:0.000000:0.000000:0.000000
Observa que :@0.293657:0.788958:0.396187:0.788958:0.396187:0.773245:0.293657:0.773245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen x:@0.398249:0.788958:0.437105:0.788958:0.437105:0.773523:0.398249:0.773523:0.000000:0.000000:0.000000:0.000000:0.000000
( )     denota el valor de la función :@0.424496:0.788958:0.719785:0.788958:0.719785:0.773245:0.424496:0.773245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[:@0.448572:0.788819:0.463905:0.788819:0.463905:0.774771:0.448572:0.774771:0.000000
R:@0.470311:0.788098:0.483601:0.788098:0.483601:0.775201:0.470311:0.775201:0.000000
Sen:@0.721846:0.788958:0.747861:0.788958:0.747861:0.773523:0.721846:0.773523:0.000000:0.000000:0.000000
 en      . Se tiene así :@0.748113:0.788958:0.930916:0.788958:0.930916:0.773245:0.748113:0.773245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.779645:0.788958:0.787100:0.788958:0.787100:0.773523:0.779645:0.773523:0.000000
[:@0.793414:0.788819:0.808747:0.788819:0.808747:0.774771:0.793414:0.774771:0.000000
R:@0.815153:0.788098:0.828443:0.788098:0.828443:0.775201:0.815153:0.775201:0.000000
 :@0.926885:0.788958:0.930916:0.788958:0.930916:0.773245:0.926885:0.773245:0.000000
Dom Sen(x:@0.293638:0.805600:0.371453:0.805600:0.371453:0.790164:0.293638:0.790164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.329036:0.805600:0.333913:0.805600:0.333913:0.789887:0.329036:0.789887:0.000000
))    .:@0.371409:0.805600:0.420556:0.805600:0.420556:0.789887:0.371409:0.789887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.384957:0.805045:0.400290:0.805045:0.400290:0.791329:0.384957:0.791329:0.000000
R:@0.404156:0.804740:0.417446:0.804740:0.417446:0.791842:0.404156:0.791842:0.000000
He aquí algunos valores típicos de :@0.293657:0.834029:0.557458:0.834029:0.557458:0.818317:0.293657:0.818317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen x:@0.558868:0.834029:0.597229:0.834029:0.597229:0.818594:0.558868:0.818594:0.000000:0.000000:0.000000:0.000000:0.000000
( ) para       que han sido obtenidos como :@0.584767:0.834029:0.930774:0.834029:0.930774:0.818317:0.584767:0.818317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.645696:0.834029:0.653150:0.834029:0.653150:0.818594:0.645696:0.818594:0.000000
[:@0.658507:0.833891:0.673840:0.833891:0.673840:0.819842:0.658507:0.819842:0.000000
R:@0.679234:0.833170:0.692524:0.833170:0.692524:0.820272:0.679234:0.820272:0.000000
relación trigonométrica en el círculo trigonométrico: :@0.293638:0.850671:0.677755:0.850671:0.677755:0.834959:0.293638:0.834959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen(0) :@0.293660:0.886575:0.343857:0.886575:0.343857:0.870862:0.293660:0.870862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 :@0.343855:0.886020:0.363790:0.886020:0.363790:0.872304:0.343855:0.872304:0.000000:0.000000
0, Sen:@0.363790:0.886575:0.407432:0.886575:0.407432:0.870862:0.363790:0.870862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
5 :@0.779223:0.886020:0.799158:0.886020:0.799158:0.872304:0.779223:0.872304:0.000000:0.000000
1,:@0.799158:0.886575:0.811344:0.886575:0.811344:0.870862:0.799158:0.870862:0.000000:0.000000
, Sen:@0.485407:0.886575:0.520068:0.886575:0.520068:0.870862:0.485407:0.870862:0.000000:0.000000:0.000000:0.000000:0.000000
5 :@0.443696:0.886020:0.463631:0.886020:0.463631:0.872304:0.443696:0.872304:0.000000:0.000000
p:@0.413563:0.878157:0.425841:0.878157:0.425841:0.864441:0.413563:0.864441:0.000000
6:@0.414981:0.894188:0.423963:0.894188:0.423963:0.878476:0.414981:0.878476:0.000000
1:@0.468032:0.878714:0.477015:0.878714:0.477015:0.863001:0.468032:0.863001:0.000000
2:@0.469449:0.894191:0.478432:0.894191:0.478432:0.878478:0.469449:0.878478:0.000000
S D:@0.406001:0.891850:0.434743:0.891850:0.434743:0.861356:0.406001:0.861356:0.000000:0.000000:0.000000
D S:@0.541954:0.891850:0.525645:0.891850:0.525645:0.861356:0.541954:0.861356:0.000000:0.000000:0.000000
D S:@0.657431:0.891850:0.642811:0.891850:0.642811:0.861356:0.657431:0.861356:0.000000:0.000000:0.000000
D S:@0.765373:0.891850:0.752175:0.891850:0.752175:0.861356:0.765373:0.861356:0.000000:0.000000:0.000000
D:@0.770159:0.932291:0.777217:0.932291:0.777217:0.901797:0.770159:0.901797:0.000000
D:@0.631885:0.933560:0.638943:0.933560:0.638943:0.903067:0.631885:0.903067:0.000000
D:@0.493293:0.932291:0.500352:0.932291:0.500352:0.901797:0.493293:0.901797:0.000000
D:@0.354670:0.932291:0.361728:0.932291:0.361728:0.901797:0.354670:0.901797:0.000000
p:@0.527819:0.878159:0.540096:0.878159:0.540096:0.864444:0.527819:0.864444:0.000000
4:@0.529236:0.894191:0.538219:0.894191:0.538219:0.878478:0.529236:0.878478:0.000000
, Sen:@0.600894:0.886575:0.635555:0.886575:0.635555:0.870862:0.600894:0.870862:0.000000:0.000000:0.000000:0.000000:0.000000
5 :@0.559183:0.886020:0.579118:0.886020:0.579118:0.872304:0.559183:0.872304:0.000000:0.000000
2:@0.585193:0.878712:0.594175:0.878712:0.594175:0.862999:0.585193:0.862999:0.000000
2:@0.584935:0.894188:0.593918:0.894188:0.593918:0.878476:0.584935:0.878476:0.000000
p:@0.643304:0.878157:0.655582:0.878157:0.655582:0.864441:0.643304:0.864441:0.000000
3:@0.644722:0.894188:0.653704:0.894188:0.653704:0.878476:0.644722:0.878476:0.000000
, Sen:@0.710258:0.886575:0.744919:0.886575:0.744919:0.870862:0.710258:0.870862:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.752668:0.878157:0.764946:0.878157:0.764946:0.864441:0.752668:0.864441:0.000000
2:@0.754086:0.894188:0.763069:0.894188:0.763069:0.878476:0.754086:0.878476:0.000000
5 :@0.670885:0.886020:0.690820:0.886020:0.690820:0.872304:0.670885:0.872304:0.000000:0.000000
3:@0.696913:0.878712:0.705896:0.878712:0.705896:0.862999:0.696913:0.862999:0.000000
2:@0.696655:0.894188:0.705638:0.894188:0.705638:0.878476:0.696655:0.878476:0.000000
Sen:@0.293660:0.927015:0.321087:0.927015:0.321087:0.911303:0.293660:0.911303:0.000000:0.000000:0.000000
5 2:@0.781451:0.926461:0.816719:0.926461:0.816719:0.912745:0.781451:0.912745:0.000000:0.000000:0.000000
1,:@0.816719:0.927015:0.828905:0.927015:0.828905:0.911303:0.816719:0.911303:0.000000:0.000000
, Sen:@0.424052:0.927015:0.458713:0.927015:0.458713:0.911303:0.424052:0.911303:0.000000:0.000000:0.000000:0.000000:0.000000
5 2 :@0.367431:0.926461:0.407301:0.926461:0.407301:0.912745:0.367431:0.912745:0.000000:0.000000:0.000000:0.000000
2:@0.321873:0.926461:0.337207:0.926461:0.337207:0.912745:0.321873:0.912745:0.000000
2:@0.460388:0.926461:0.475721:0.926461:0.475721:0.912745:0.460388:0.912745:0.000000
2:@0.598037:0.926599:0.613371:0.926599:0.613371:0.912884:0.598037:0.912884:0.000000
2:@0.657438:0.926599:0.672771:0.926599:0.672771:0.912884:0.657438:0.912884:0.000000
2:@0.735356:0.926599:0.750689:0.926599:0.750689:0.912884:0.735356:0.912884:0.000000
2:@0.522384:0.926599:0.537717:0.926599:0.537717:0.912884:0.522384:0.912884:0.000000
p:@0.340557:0.918597:0.352834:0.918597:0.352834:0.904882:0.340557:0.904882:0.000000
6:@0.341974:0.934629:0.350957:0.934629:0.350957:0.918916:0.341974:0.918916:0.000000
1:@0.406681:0.919154:0.415663:0.919154:0.415663:0.903442:0.406681:0.903442:0.000000
2:@0.408098:0.934631:0.417081:0.934631:0.417081:0.918918:0.408098:0.918918:0.000000
S:@0.319609:0.932290:0.326668:0.932290:0.326668:0.901796:0.319609:0.901796:0.000000
S:@0.457247:0.932290:0.464305:0.932290:0.464305:0.901796:0.457247:0.901796:0.000000
S :@0.594980:0.932290:0.609987:0.932290:0.609987:0.901796:0.594980:0.901796:0.000000:0.000000
p:@0.479647:0.918724:0.491925:0.918724:0.491925:0.905008:0.479647:0.905008:0.000000
4:@0.481056:0.934752:0.490039:0.934752:0.490039:0.919039:0.481056:0.919039:0.000000
, Sen:@0.559436:0.927015:0.594097:0.927015:0.594097:0.911303:0.559436:0.911303:0.000000:0.000000:0.000000:0.000000:0.000000
5 :@0.505410:0.926461:0.525346:0.926461:0.525346:0.912745:0.505410:0.912745:0.000000:0.000000
2:@0.543550:0.919208:0.552533:0.919208:0.552533:0.903495:0.543550:0.903495:0.000000
2:@0.543281:0.934677:0.552264:0.934677:0.552264:0.918964:0.543281:0.918964:0.000000
p:@0.616808:0.918862:0.629085:0.918862:0.629085:0.905146:0.616808:0.905146:0.000000
3:@0.618218:0.934891:0.627201:0.934891:0.627201:0.919178:0.618218:0.919178:0.000000
, Sen:@0.694851:0.927015:0.729512:0.927015:0.729512:0.911303:0.694851:0.911303:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.756019:0.918597:0.768296:0.918597:0.768296:0.904882:0.756019:0.904882:0.000000
2:@0.757436:0.934629:0.766419:0.934629:0.766419:0.918916:0.757436:0.918916:0.000000
S:@0.731003:0.932290:0.738061:0.932290:0.738061:0.901796:0.731003:0.901796:0.000000
5 :@0.638774:0.926461:0.658709:0.926461:0.658709:0.912745:0.638774:0.912745:0.000000:0.000000
3:@0.681498:0.919152:0.690480:0.919152:0.690480:0.903440:0.681498:0.903440:0.000000
2:@0.681240:0.934629:0.690223:0.934629:0.690223:0.918916:0.681240:0.918916:0.000000
Tema 2. Funciones trigonométricas:@0.073089:0.098522:0.591631:0.098522:0.591631:0.067281:0.073089:0.067281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Basta conocer la gráfica :@0.082576:0.289604:0.242115:0.289604:0.242115:0.275320:0.082576:0.275320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la función periódica en :@0.082576:0.304733:0.259049:0.304733:0.259049:0.290449:0.082576:0.290449:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el intervalo :@0.082576:0.319862:0.159868:0.319862:0.159868:0.305578:0.082576:0.305578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
F:@0.159834:0.320392:0.163549:0.320392:0.163549:0.304343:0.159834:0.304343:0.000000
2p p:@0.163549:0.319358:0.206388:0.319358:0.206388:0.306889:0.163549:0.306889:0.000000:0.000000:0.000000:0.000000
,    y lu-:@0.188650:0.319862:0.245679:0.319862:0.245679:0.305578:0.188650:0.305578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
G:@0.206388:0.320392:0.210103:0.320392:0.210103:0.304343:0.206388:0.304343:0.000000
ego reproducir en forma :@0.082576:0.334991:0.248741:0.334991:0.248741:0.320707:0.082576:0.320707:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
idéntica al lado izquierdo :@0.082576:0.350120:0.252543:0.350120:0.252543:0.335836:0.082576:0.335836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y al lado derecho en in-:@0.082576:0.365249:0.237749:0.365249:0.237749:0.350965:0.082576:0.350965:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tervalos de longitud 2 .:@0.082576:0.380378:0.241815:0.380378:0.241815:0.366094:0.082576:0.366094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
p:@0.227742:0.379874:0.238904:0.379874:0.238904:0.367405:0.227742:0.367405:0.000000
Competencia :@0.078576:0.250849:0.177268:0.250849:0.177268:0.235443:0.078576:0.235443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática :@0.078576:0.265978:0.167191:0.265978:0.167191:0.250572:0.078576:0.250572:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si en una función periódica conoces la forma de gráfica en un intervalo 2T, :@0.293660:0.162175:0.867646:0.162175:0.867646:0.146462:0.293660:0.146462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿cómo reproduces la gráfica de la función al lado positivo y al lado negativo de :@0.293660:0.178817:0.867856:0.178817:0.867856:0.163104:0.293660:0.163104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los números reales?:@0.293660:0.195458:0.435696:0.195458:0.435696:0.179746:0.293660:0.179746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 4 (Ev. 4) Reconoce algunas aplicaciones de las funciones trigonométricas en el estudio de fenómenos diversos de :@0.260930:0.966323:0.885615:0.966323:0.885615:0.954896:0.260930:0.954896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variación periódica, por ejemplo: movimiento circular, movimiento del péndulo, del pistón, ciclo de la respiración, entre otros.:@0.260930:0.976409:0.919835:0.976409:0.919835:0.964982:0.260930:0.964982:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Reto matemático:@0.302768:0.139665:0.425244:0.139665:0.425244:0.124259:0.302768:0.124259:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Amplitud:@0.084459:0.526030:0.153453:0.524668:0.152900:0.508762:0.083906:0.510123:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Valor máx-:@0.153452:0.524669:0.233247:0.523095:0.232726:0.508101:0.152930:0.509676:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
imo de una cantidad :@0.085010:0.541911:0.233993:0.538971:0.233471:0.523978:0.084489:0.526917:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable, o la diferencia :@0.085562:0.557791:0.248157:0.554582:0.247636:0.539589:0.085041:0.542797:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
entre el valor máxi-:@0.086114:0.573670:0.219728:0.571034:0.219206:0.556041:0.085593:0.558677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
mo y mínimo de una :@0.086666:0.589550:0.237019:0.586584:0.236497:0.571590:0.086145:0.574557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función periódica, :@0.087218:0.605430:0.217141:0.602867:0.216620:0.587873:0.086697:0.590437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
o como el despla-:@0.087770:0.621310:0.213058:0.618838:0.212537:0.603845:0.087249:0.606317:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
zamiento máximo :@0.088322:0.637190:0.219020:0.634611:0.218499:0.619618:0.087801:0.622197:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
en un movimiento :@0.088874:0.653070:0.222997:0.650424:0.222476:0.635430:0.088353:0.638077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
armónico simple.:@0.089426:0.668950:0.209972:0.666572:0.209450:0.651578:0.088905:0.653957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
periódico:@0.090227:0.691976:0.160012:0.690599:0.159459:0.674693:0.089674:0.676070:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Dicho de :@0.160012:0.690599:0.234310:0.689133:0.233789:0.674140:0.159491:0.675606:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
un fenómeno de fases :@0.090779:0.707856:0.250458:0.704705:0.249937:0.689712:0.090257:0.692863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
que se repiten con :@0.091331:0.723736:0.225873:0.721081:0.225352:0.706088:0.090810:0.708743:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
regularidad.:@0.091883:0.739616:0.174891:0.737978:0.174370:0.722985:0.091362:0.724623:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.137491:0.502307:0.197111:0.502307:0.197111:0.486901:0.137491:0.486901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
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