Question

One of the roots of the equation 8x^3 −6x+1=0 is:
A) sin 250° B) sin 40° C) sin 70° D) sin 160° E) sin 10°

Answer 1

8x^3 - 6x + 1 = 0
8x^3 - 6x = -1
4x^3 - 3x = -1/2
3x - 4x^3 = 1/2
somehow we have to connect this to trig.

recall sin(3θ) = 3sinθ - 4sin^3 θ

if we let sinθ = x, we have
sin 3θ = 1/2 , ........ recall sin 30° = 1/2
then 3θ = sin 30°
3θ = 30°

θ = 10°

then sin 10° is a solution to your equation.

Answer 2

4th last line should say:

then sin 3θ = sin 30°