solve the following trigonometric equation for all angles, where 0<theta<2pi

Question

2 sin^2 theta- 3 sin theta=2

Answer 1

X instead oh angle theta

Let U = sin x

2u^2- 3u=2

2u^2- 3u-2=0

( 2u. +1 )( u - 2)=0

2u+1=0 or u-2=0

U=1/2 or u=2

Sine cannot be 2

Sine is 1/2 at 30 And 150 degrees

Pi/6 or 5*pi/6