Alguien puede ayudarme a resolver esta ecuacion trigonometrica : 2sen ^ 2(t) - cos(t) - 1 = 0 ?
Alguien puede ayudarme a resolver esta ecuacion trigonometrica : 2sen ^ 2(t) - cos(t) - 1 = 0 ?
0Germanhdzpo9571
Calculadora: Calculadora de ecuaciones de segundo grado
Calculadora interactiva
ax² + bx + c = 0
Mejor respuesta
Valerinuo24
<img src="https://tex.z-dn.net/?f=2sen%5E%7B2%7D%28t%29-cos%28t%29-1%3D0" />
Si <img src="https://tex.z-dn.net/?f=sen%5E%7B2%7D%28t%29%3D1-cos%5E%7B2%7D%28t%29%20" /> remplazo el equivalente en<img src="https://tex.z-dn.net/?f=sen%20%5E%7B2%7D%28t%29%20" />
<img src="https://tex.z-dn.net/?f=%20%202%281-cos%5E%7B2%7D%20%28t%29%29-cos%28t%29-1%3D0" />
Propiedad distributiva
<img src="https://tex.z-dn.net/?f=%202-2cos%5E%7B2%7D%20%28t%29-cos%28t%29-1%3D0" />
<img src="https://tex.z-dn.net/?f=%20-2cos%5E%7B2%7D%20%28t%29-cos%28t%29%2B1%3D0" />
Cambio de variable
cost = x
<img src="https://tex.z-dn.net/?f=-2%20x%5E%7B2%7D%20-x%2B1%3D0%0A" />
multiplico por - <img src="https://tex.z-dn.net/?f=-2%20x%5E%7B2%7D%20-x%2B1%3D0%20" />⇔<img src="https://tex.z-dn.net/?f=2%20x%5E%7B2%7D%20%2Bx-1%3D0%20" />
Factorizando
(x + 1)(2x - 1) = 0
x + 1 = 0 2x - 1 = 0
x = - 1 x = <img src="https://tex.z-dn.net/?f=%20%5Cfrac%7B1%7D%7B2%7D%20" />
Si
Cost = x cost = x
cost = - 1 cost = [img = 10]
t = cos'( - 1) t = cos'[img = 11]
t = 180° = π t = 60° = [img = 12]
Sol.
T = [img = 13], [img = 14].