Solve 2sin x-3sinx+1=0 for principal values of x

Question

A. 0°,30°

B. 30°

C. 30°,  90°

D. 0°, 60°

Answer 1

Assuming you actually meant 2SIN²(x) instead, here is the method and answer:

Try replacing "SIN(x)" with a variable like "U" so it reads 2U² - 3U + 1 = 0   to make it easy on the eyes.

Factor by un-foiling: (2U -1) (U-1) = 0 and set each to zero separately.

This yields U = 1/2   and U = 1  . Switch back to SIN(x) and you get:

SIN(x) = 1/2   and SIN(x) = 1

The SIN function equals 1/2 at 30° (and again at 150°), while it equals 1 at 90°

So: answer C