Find all solutions of the equation 3sin^2 x -7sin x +2 = 0 in the interval [0,2pi).

Question

The answer is x_1= ?? and x_2= ?? with x_1<x_2.

Answer 1

3 z^2 - 7 z + 2 = 0

(3 z - 1)(z - 2) = 0
z = 1/3 or z = 2

so if sin x = 1/3
x = .34 radians or pi - .34 = 2.8 radians

sin x = 2 has no solutions