Solve the following equation for all radian solutions and if

Solve the following equation for all radian solutions and if 0 x < 2. Give all answers as exact values in radians. Do not use a calculator. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

2 sin²x + sin x 1 = 0

(a)    all radian solutions (Let k be any integer.)
x = rad

(b)    0 x < 2
x = rad

Solution

2sin^2x +sin x-1=0

2sin^2x +2sinx -sinx-1=0

2sinx(sin x+1) -1(sinx+1)=0

(2sinx-1)(sinx+1)=0

Sin x=1/2 ,sinx=-1

x=pi/6,5pi/6,3pi/2