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