172:@0.053974:0.966765:0.079386:0.966765:0.079386:0.950778:0.053974:0.950778:0.000000:0.000000:0.000000
Funciones trigonométricas :@0.404235:0.128735:0.737942:0.128735:0.737942:0.084076:0.404235:0.084076:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En este capítulo definiremos las funciones trigonométricas: seno, :@0.404236:0.160704:0.895939:0.160704:0.895939:0.144206:0.404236:0.144206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coseno, tangente, cotangente, secante y cosecante. Se observarán :@0.404236:0.176421:0.895949:0.176421:0.895949:0.159923:0.404236:0.159923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
algunas propiedades, por ejemplo, la periodicidad, y se construirán :@0.404236:0.192138:0.895920:0.192138:0.895920:0.175640:0.404236:0.175640:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
funciones trigonométricas. :@0.404236:0.207854:0.597869:0.207854:0.597869:0.191357:0.404236:0.191357:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Funciones periódicas:@0.404236:0.239928:0.572815:0.239928:0.572815:0.222246:0.404236:0.222246:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Iniciamos el estudio con una clase de funciones denominadas perió-:@0.404236:0.255001:0.891770:0.255001:0.891770:0.238504:0.404236:0.238504:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dicas, cuya definición se da a continuación.:@0.404236:0.270718:0.709298:0.270718:0.709298:0.254221:0.404236:0.254221:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
  :@0.404236:0.286435:0.412520:0.286435:0.412520:0.269937:0.404236:0.269937:0.000000:0.000000
Definición :@0.404236:0.302615:0.491103:0.302615:0.491103:0.285669:0.404236:0.285669:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sean   > 0 y   una función real definida en todo  . Se :@0.484322:0.302152:0.895907:0.302150:0.895907:0.285652:0.484322:0.285654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.531984:0.302268:0.541790:0.302268:0.541790:0.285799:0.531984:0.285799:0.000000
f:@0.591726:0.302268:0.596022:0.302268:0.596022:0.285799:0.591726:0.285799:0.000000
R:@0.853666:0.301063:0.866971:0.301063:0.866971:0.288201:0.853666:0.288201:0.000000
dice que   es periódica de período 2  si y solo si   verifica la siguiente :@0.404239:0.317867:0.895940:0.317867:0.895940:0.301369:0.404239:0.301369:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f:@0.469432:0.317983:0.473728:0.317983:0.473728:0.301514:0.469432:0.301514:0.000000
T:@0.659711:0.317983:0.669517:0.317983:0.669517:0.301514:0.659711:0.301514:0.000000
f:@0.749081:0.317983:0.753377:0.317983:0.753377:0.301514:0.749081:0.301514:0.000000
condición::@0.404239:0.333584:0.478429:0.333584:0.478429:0.317086:0.404239:0.317086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.557089:0.349417:0.574813:0.349417:0.574813:0.332948:0.557089:0.332948:0.000000:0.000000:0.000000
(  + 2 ) =  ( ),         .:@0.561385:0.349301:0.738911:0.349299:0.738911:0.332801:0.561385:0.332803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.602401:0.349417:0.612207:0.349417:0.612207:0.332948:0.602401:0.332948:0.000000
f x:@0.637252:0.349417:0.654976:0.349417:0.654976:0.332948:0.637252:0.332948:0.000000:0.000000:0.000000
∀:@0.680255:0.356885:0.691828:0.356885:0.691828:0.337886:0.680255:0.337886:0.000000
x:@0.691836:0.349415:0.699311:0.349415:0.699311:0.332946:0.691836:0.332946:0.000000
:@0.703452:0.348780:0.718105:0.348780:0.718105:0.335407:0.703452:0.335407:0.000000
R:@0.722246:0.348330:0.736156:0.348330:0.736156:0.334883:0.722246:0.334883:0.000000
  :@0.404235:0.365016:0.412519:0.365016:0.412519:0.348518:0.404235:0.348518:0.000000:0.000000
En la Figura 5.1., se representa una función periódica de período 2 .:@0.404235:0.380733:0.881025:0.380733:0.881025:0.364235:0.404235:0.364235:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.868464:0.380848:0.878270:0.380848:0.878270:0.364380:0.868464:0.364380:0.000000
La característica fundamental de las funciones periódicas es que bas-:@0.404235:0.506468:0.891761:0.506468:0.891761:0.489970:0.404235:0.489970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ta conocer la función en un intervalo de longitud 2 , por ejemplo :@0.404235:0.522185:0.895921:0.522185:0.895921:0.505687:0.404235:0.505687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.783831:0.522300:0.793637:0.522300:0.793637:0.505832:0.783831:0.505832:0.000000
[– ,  ], y luego reproducir esta porción de función del lado positi-:@0.404235:0.537902:0.891792:0.537902:0.891792:0.521404:0.404235:0.521404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T T:@0.420783:0.538017:0.448641:0.538017:0.448641:0.521549:0.420783:0.521549:0.000000:0.000000:0.000000
vo de los números reales a intervalos de la formas [ , 3 ], [3 , 5 ], :@0.404235:0.553619:0.895922:0.553619:0.895922:0.537121:0.404235:0.537121:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T T:@0.781096:0.553734:0.817628:0.553734:0.817628:0.537265:0.781096:0.537265:0.000000:0.000000:0.000000
T T:@0.846449:0.553734:0.882976:0.553734:0.882976:0.537265:0.846449:0.537265:0.000000:0.000000:0.000000
[5 , 7 ] y así sucesivamente; a continuación , del lado negativo a :@0.404254:0.569335:0.895992:0.569335:0.895992:0.552838:0.404254:0.552838:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T T:@0.418799:0.569451:0.456501:0.569451:0.456501:0.552982:0.418799:0.552982:0.000000:0.000000:0.000000
intervalos de la formas [–3 , – ], [–5 , –3 ], y así sucesivamente. La :@0.404254:0.585052:0.895880:0.585052:0.895880:0.568555:0.404254:0.568555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T T:@0.594901:0.585168:0.632142:0.585168:0.632142:0.568699:0.594901:0.568699:0.000000:0.000000:0.000000
T:@0.670230:0.585168:0.680036:0.585168:0.680036:0.568699:0.670230:0.568699:0.000000
T:@0.706217:0.585168:0.716023:0.585168:0.716023:0.568699:0.706217:0.568699:0.000000
gráfica de la función periódica en el intervalo [– ,  ] se reproduce :@0.404235:0.600769:0.895921:0.600769:0.895921:0.584272:0.404235:0.584272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T T:@0.757979:0.600885:0.785937:0.600885:0.785937:0.584416:0.757979:0.584416:0.000000:0.000000:0.000000
sucesivamente a cada uno de los intervalos de los tipos antes indica-:@0.404235:0.616486:0.891782:0.616486:0.891782:0.599988:0.404235:0.599988:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos. Las funciones trigonométricas son funciones periódicas. :@0.404235:0.632203:0.838425:0.632203:0.838425:0.615705:0.404235:0.615705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Función seno, gráfico y características:@0.404236:0.664267:0.706656:0.664267:0.706656:0.646585:0.404236:0.646585:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Esta función se designa con :@0.404236:0.679340:0.603936:0.679340:0.603936:0.662843:0.404236:0.662843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen:@0.603936:0.679456:0.628711:0.679456:0.628711:0.662987:0.603936:0.662987:0.000000:0.000000:0.000000
 y se define como sigue::@0.628715:0.679340:0.796901:0.679340:0.796901:0.662843:0.628715:0.662843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sen:                       :@0.584713:0.710774:0.708550:0.710774:0.708550:0.694277:0.584713:0.694277:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. ):@0.708550:0.719580:0.705672:0.720301:0.705672:0.703803:0.708550:0.703082:0.000000:0.000000:0.000000
Observa que sen( )     denota el valor de la función :@0.404236:0.742208:0.793738:0.742206:0.793738:0.725708:0.404236:0.725710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.529593:0.742324:0.537068:0.742324:0.537068:0.725855:0.529593:0.725855:0.000000
:@0.547281:0.741991:0.563329:0.741991:0.563329:0.727344:0.547281:0.727344:0.000000
R:@0.568346:0.741119:0.581651:0.741119:0.581651:0.728256:0.568346:0.728256:0.000000
sen:@0.793854:0.742321:0.816856:0.742321:0.816856:0.725852:0.793854:0.725852:0.000000:0.000000:0.000000
 en      . :@0.816841:0.742206:0.895912:0.742206:0.895912:0.725708:0.816841:0.725708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.842907:0.742321:0.850382:0.742321:0.850382:0.725852:0.842907:0.725852:0.000000
:@0.854639:0.741989:0.870687:0.741989:0.870687:0.727342:0.854639:0.727342:0.000000
R:@0.875711:0.741119:0.889015:0.741119:0.889015:0.728256:0.875711:0.728256:0.000000
Se tiene así :@0.404244:0.757922:0.486620:0.757922:0.486620:0.741425:0.404244:0.741425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Dom:@0.486620:0.758038:0.521837:0.758038:0.521837:0.741569:0.486620:0.741569:0.000000:0.000000:0.000000
(Sen) =  .:@0.521839:0.757922:0.594700:0.757922:0.594700:0.741424:0.521839:0.741425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.578642:0.756835:0.591947:0.756835:0.591947:0.743973:0.578642:0.743973:0.000000
He aquí algunos valores típicos de sen( ) para       que han sido :@0.404244:0.789356:0.895899:0.789354:0.895899:0.772857:0.404244:0.772858:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.687422:0.789471:0.694897:0.789471:0.694897:0.773002:0.687422:0.773002:0.000000
x:@0.743135:0.789471:0.750610:0.789471:0.750610:0.773002:0.743135:0.773002:0.000000
:@0.756162:0.789139:0.772210:0.789139:0.772210:0.774492:0.756162:0.774492:0.000000
R:@0.778510:0.788267:0.791815:0.788267:0.791815:0.775405:0.778510:0.775405:0.000000
obtenidos como relación trigonométrica en el círculo trigonométrico: :@0.404235:0.805071:0.895965:0.805071:0.895965:0.788574:0.404235:0.788574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen(0) = 0,  sen       =     ,  sen       =       ,  sen       =       ,  sen       = 1, :@0.404235:0.836505:0.891856:0.836505:0.891856:0.820007:0.404235:0.820007:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sen  –      = –     ,  sen  –      = –       ,  sen  –      = –       ,  sen  –      = –1.:@0.404235:0.882195:0.891792:0.882195:0.891792:0.865698:0.404235:0.865698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
R:@0.629824:0.701863:0.643129:0.701863:0.643129:0.689001:0.629824:0.689001:0.000000
    ,:@0.643129:0.702950:0.683613:0.702950:0.683613:0.686452:0.643129:0.686452:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.647271:0.711049:0.663415:0.711049:0.663415:0.691186:0.647271:0.691186:0.000000
R:@0.667555:0.701863:0.680860:0.701863:0.680860:0.689001:0.667555:0.689001:0.000000
x   sen(:@0.629825:0.720301:0.692244:0.720301:0.692244:0.703803:0.629825:0.703803:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.641962:0.728400:0.658106:0.728400:0.658106:0.708537:0.641962:0.708537:0.000000
x:@0.692244:0.720416:0.699719:0.720416:0.699719:0.703948:0.692244:0.703948:0.000000
π:@0.452771:0.874553:0.463174:0.874553:0.463174:0.858055:0.452771:0.858055:0.000000
6:@0.453715:0.890891:0.462211:0.890891:0.462211:0.874394:0.453715:0.874394:0.000000
π:@0.575064:0.874553:0.585467:0.874553:0.585467:0.858055:0.575064:0.858055:0.000000
4:@0.576008:0.890891:0.584504:0.890891:0.584504:0.874394:0.576008:0.874394:0.000000
π:@0.705148:0.874553:0.715551:0.874553:0.715551:0.858055:0.705148:0.858055:0.000000
3:@0.706092:0.890891:0.714588:0.890891:0.714588:0.874394:0.706092:0.874394:0.000000
π:@0.835816:0.874553:0.846220:0.874553:0.846220:0.858055:0.835816:0.858055:0.000000
2:@0.836760:0.890891:0.845256:0.890891:0.845256:0.874394:0.836760:0.874394:0.000000
1:@0.503665:0.874553:0.512161:0.874553:0.512161:0.858055:0.503665:0.858055:0.000000
2:@0.503665:0.890891:0.512161:0.890891:0.512161:0.874394:0.503665:0.874394:0.000000
 2:@0.626736:0.874553:0.639374:0.874553:0.639374:0.858055:0.626736:0.858055:0.000000:0.000000
2:@0.628798:0.890891:0.637294:0.890891:0.637294:0.874394:0.628798:0.874394:0.000000
 3:@0.757405:0.874553:0.770043:0.874553:0.770043:0.858055:0.757405:0.858055:0.000000:0.000000
2:@0.759467:0.890891:0.767963:0.890891:0.767963:0.874394:0.759467:0.874394:0.000000
π:@0.522128:0.829422:0.532531:0.829422:0.532531:0.812924:0.522128:0.812924:0.000000
6:@0.523072:0.845761:0.531568:0.845761:0.531568:0.829263:0.523072:0.829263:0.000000
π:@0.621955:0.829422:0.632359:0.829422:0.632359:0.812924:0.621955:0.812924:0.000000
4:@0.622899:0.845761:0.631395:0.845761:0.631395:0.829263:0.622899:0.829263:0.000000
π:@0.839485:0.829422:0.849888:0.829422:0.849888:0.812924:0.839485:0.812924:0.000000
2:@0.840429:0.845761:0.848925:0.845761:0.848925:0.829263:0.840429:0.829263:0.000000
π:@0.730846:0.829422:0.741249:0.829422:0.741249:0.812924:0.730846:0.812924:0.000000
3:@0.731790:0.845761:0.740286:0.845761:0.740286:0.829263:0.731790:0.829263:0.000000
1:@0.561519:0.829422:0.570015:0.829422:0.570015:0.812924:0.561519:0.812924:0.000000
2:@0.561519:0.845761:0.570015:0.845761:0.570015:0.829263:0.561519:0.829263:0.000000
 2:@0.663325:0.829422:0.675963:0.829422:0.675963:0.812924:0.663325:0.812924:0.000000:0.000000
2:@0.665387:0.845761:0.673883:0.845761:0.673883:0.829263:0.665387:0.829263:0.000000
 3:@0.773891:0.829422:0.786529:0.829422:0.786529:0.812924:0.773891:0.812924:0.000000:0.000000
2:@0.775953:0.845761:0.784449:0.845761:0.784449:0.829263:0.775953:0.829263:0.000000
p:@0.828839:0.476201:0.840320:0.476201:0.840320:0.466177:0.828839:0.466177:0.000000
 :@0.840320:0.476909:0.843201:0.476909:0.843201:0.465433:0.840320:0.465433:0.000000
Figura 5.1.:@0.843201:0.476909:0.891769:0.476909:0.891769:0.465433:0.843201:0.465433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.578237:0.408424:0.584698:0.408424:0.584698:0.394795:0.578237:0.394795:0.000000
x:@0.876002:0.457455:0.882607:0.457455:0.882607:0.443827:0.876002:0.443827:0.000000
0:@0.581054:0.456177:0.588072:0.456177:0.588072:0.442549:0.581054:0.442549:0.000000
–:@0.529037:0.457923:0.536341:0.457923:0.536341:0.446446:0.529037:0.446446:0.000000
T:@0.536341:0.458003:0.543162:0.458003:0.543162:0.446547:0.536341:0.446547:0.000000
–2:@0.471475:0.457923:0.484690:0.457923:0.484690:0.446446:0.471475:0.446446:0.000000:0.000000
T:@0.484690:0.458003:0.491511:0.458003:0.491511:0.446547:0.484690:0.446547:0.000000
–3:@0.416862:0.457923:0.430077:0.457923:0.430077:0.446446:0.416862:0.446446:0.000000:0.000000
T:@0.430077:0.458003:0.436898:0.458003:0.436898:0.446547:0.430077:0.446547:0.000000
T:@0.641907:0.458003:0.648729:0.458003:0.648729:0.446547:0.641907:0.446547:0.000000
2:@0.693558:0.457923:0.699469:0.457923:0.699469:0.446446:0.693558:0.446446:0.000000
T:@0.699469:0.458003:0.706290:0.458003:0.706290:0.446547:0.699469:0.446547:0.000000
3:@0.748171:0.457923:0.754082:0.457923:0.754082:0.446446:0.748171:0.446446:0.000000
T:@0.754082:0.458003:0.760903:0.458003:0.760903:0.446547:0.754082:0.446547:0.000000
4:@0.802784:0.457923:0.808694:0.457923:0.808694:0.446446:0.802784:0.446446:0.000000
T:@0.808694:0.458003:0.815516:0.458003:0.815516:0.446547:0.808694:0.446547:0.000000
5:@0.857397:0.457923:0.863307:0.457923:0.863307:0.446446:0.857397:0.446446:0.000000
T:@0.863307:0.458003:0.870129:0.458003:0.870129:0.446547:0.863307:0.446547:0.000000
y f x:@0.675685:0.413805:0.714383:0.413805:0.714383:0.399485:0.675685:0.399485:0.000000:0.000000:0.000000:0.000000:0.000000
 =  ( ):@0.682370:0.413705:0.719560:0.413705:0.719560:0.399359:0.682370:0.399359:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Saberes previos:@0.199644:0.112641:0.307803:0.112641:0.307803:0.097169:0.199644:0.097169:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿Qué es una función :@0.199880:0.141268:0.336907:0.141268:0.336907:0.126205:0.199880:0.126205:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
periódica?:@0.153337:0.157110:0.219421:0.157110:0.219421:0.142047:0.153337:0.142047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Desequilibrio cognitivo:@0.199646:0.207816:0.363493:0.207816:0.363493:0.192344:0.199646:0.192344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Si en una función :@0.199884:0.236444:0.316627:0.236444:0.316627:0.221381:0.199884:0.221381:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
periódica conoces la forma :@0.153341:0.252286:0.332597:0.252286:0.332597:0.237223:0.153341:0.237223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de gráfica en un intervalo 2T, :@0.153341:0.268128:0.344173:0.268128:0.344173:0.253065:0.153341:0.253065:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
¿cómo reproduces la gráfica de :@0.153341:0.283970:0.358138:0.283970:0.358138:0.268907:0.153341:0.268907:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la función al lado positivo y al :@0.153341:0.299812:0.349151:0.299812:0.349151:0.284748:0.153341:0.284748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
lado negativo de los números :@0.153341:0.315654:0.348606:0.315654:0.348606:0.300590:0.153341:0.300590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
reales?:@0.153341:0.331496:0.194607:0.331496:0.194607:0.316432:0.153341:0.316432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Glosario:@0.199646:0.464984:0.267111:0.464984:0.267111:0.447301:0.199646:0.447301:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
amplitud. :@0.199884:0.491797:0.268713:0.491797:0.268713:0.476536:0.199884:0.476536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Distancia o :@0.268713:0.491599:0.344665:0.491599:0.344665:0.476536:0.268713:0.476536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valor máximo de una cantidad :@0.153341:0.507441:0.356240:0.507441:0.356240:0.492378:0.153341:0.492378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
variable, de su valor medio o :@0.153341:0.523283:0.342219:0.523283:0.342219:0.508220:0.153341:0.508220:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
valor base, o la mitad del valor :@0.153341:0.539125:0.353758:0.539125:0.353758:0.524062:0.153341:0.524062:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
máximo pico a pico de una :@0.153341:0.554967:0.334498:0.554967:0.334498:0.539904:0.153341:0.539904:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
función periódica, como un :@0.153341:0.570809:0.338155:0.570809:0.338155:0.555746:0.153341:0.555746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
movimiento armónico simple.:@0.153341:0.586651:0.349204:0.586651:0.349204:0.571588:0.153341:0.571588:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
periódicos:@0.153341:0.602691:0.224000:0.602691:0.224000:0.587430:0.153341:0.587430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Dicho de un fenó-:@0.224000:0.602493:0.349063:0.602493:0.349063:0.587430:0.224000:0.587430:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
meno de fases que se repiten :@0.153341:0.618335:0.345457:0.618335:0.345457:0.603272:0.153341:0.603272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
con regularidad.:@0.153341:0.634177:0.257067:0.634177:0.257067:0.619114:0.153341:0.619114:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.146910:0.468716:0.158315:0.467206:0.153112:0.445061:0.141707:0.446571:0.000000
c:@0.150296:0.480035:0.161046:0.478612:0.155884:0.456637:0.145134:0.458060:0.000000
b:@0.160667:0.472467:0.173381:0.470785:0.168249:0.448942:0.155535:0.450624:0.000000
M.5.1.70. Definir las funciones seno y coseno a partir de las relaciones trigonométricas en el círculo trigonométrico (unidad) e identificar sus respectivas gráficas a partir  :@0.143847:0.937859:0.891223:0.937859:0.891223:0.927817:0.143847:0.927817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del análisis de sus características particulares.  :@0.143847:0.946660:0.328706:0.946660:0.328706:0.936618:0.143847:0.936618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
M.5.1.71. Reconocer y graficar funciones periódicas determinando el período y amplitud de estas, su dominio y recorrido, monotonía y paridad.:@0.143847:0.955461:0.729534:0.955461:0.729534:0.945419:0.143847:0.945419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.200180:0.746436:0.297803:0.746436:0.297803:0.730964:0.200180:0.730964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
matemática:@0.200180:0.759004:0.284243:0.759004:0.284243:0.743532:0.200180:0.743532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Basta conocer la gráfica :@0.200418:0.783479:0.355631:0.783479:0.355631:0.768416:0.200418:0.768416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de la función en el intervalo :@0.153875:0.799321:0.336686:0.799321:0.336686:0.784258:0.153875:0.784258:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[–π, π]  y luego reproducir en :@0.153875:0.815163:0.348929:0.815163:0.348929:0.800100:0.153875:0.800100:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
forma idéntica al lado izquierdo :@0.153875:0.831005:0.361645:0.831005:0.361645:0.815942:0.153875:0.815942:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y al lado derecho en intervalos :@0.153875:0.846847:0.353836:0.846847:0.353836:0.831784:0.153875:0.831784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de longitud 2π.:@0.153875:0.862689:0.252008:0.862689:0.252008:0.847626:0.153875:0.847626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000