Question

Find all solutions in the interval [0, 2π).

sin^2 x + sin x = 0

Answer 1

Factoring:-

sin x( sin x + 1) = 0

sin x = 0 , or sinx + 1 = 0 giving sin x = -1

when sin x = 0 x = 0 , pi

when sin x = -1, x = pi + pi/2 = 3pi/2

solutions in given interval are 0,pi and 3pi/2