Mathematics

Problem

Solve the trigonometric equation

2\sin^{2}x - 3\sin x + 1 = 0

. a. (a) Obtain the general solution of the equation. b. (b) How many solutions of the equation obtained in part (a) lie in the interval

\left[-\dfrac{\pi}{2},\,\dfrac{3\pi}{2}\right]

? List all such solutions with justification.