Question

$x=arccos(-\frac{\sqrt{3}}{2})$, o valor de $cos10x$ é:


a) $\frac{\sqrt{3}}{2}$

b) $\frac{1}{2}$

c) $-\frac{1}{2}$

d) $-\frac{\sqrt{3}}{2}$

e) -1

Answer 1

Resposta:

b

Explicação passo-a-passo:

Se x = arc cos(-√3/2), então cosx = -√3/2. Logo cosx = cos5π/6 e x =5π/6

cos10x = cos10.5π/6

cos10x = cos50π/6

cos10x = cos(48π/6 + 2π/6)

cos10x = cos(8π + π/3)

cos10x = cos(π/3)

cos10x = cos(60)

cos10x = 1/2