Dos relaciones entre razones trigonométricas

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[/img][br][br]Estas relaciones permiten conocer el seno, coseno y tangente de un ángulo a partir del conocimiento de uno de ellos siempre que se sepa en qué cuadrante se encuentra el ángulo
EJEMPLOS
1.- Sabiendo que [math]\alpha[/math] es un ángulo agudo y cos [math]\alpha[/math]=0,63, calcular sen [math]\alpha[/math] y tg[math]\alpha[/math] [br][br]2- Sabiendo que [math]\alpha[/math] es un ángulo agudo y tg [math]\alpha[/math]=2, calcular sen[math]\alpha[/math] y cos[math]\alpha[/math][br][math]\alpha[/math] es un ángulo agudo y cos [math]\alpha[/math]=0,63, calcular sen [math]\alpha[/math] y tg[math]\alpha[/math]
EJERCICIOS
[b]1,2,3,4,5,6 y 7 pág 139[br][br]1 y 2 pág 140 y 141[/b]

資訊: Dos relaciones entre razones trigonométricas