The given trigonometric equations on the interval 0 2pi 2 si

The given trigonometric equations on the interval [0, 2pi) 2 sin^2 x - sin x = 0

Solution

2 sin^2 x - sin x = 0

taking the gcf sin x out

sin x ( 2 sin x - 1 ) = 0

sin x = 0   

x = 2pi*n , pi+ 2pi*n

2 sin x -1 =0

sin x = 1/2

x = pi/6 + 2pi*n , 5pi/6 + 2pi*n

solutions are

x =0, 2pi , pi/6 , 5pi/6 , pi