Find all real numbers in the interval 0 2 pi that satisfy th

Find all real numbers in the interval [0, 2 pi) that satisfy the equation. Use radian measure. 7 sin^x - 2sinx = cos^2x The solution set is (Round to the nearest tenth as needed Use a comma to separate answers as needed)

Solution

7sin^2 x -2sin x=cos^2 x

7sin^2 x -2sin x= 1-sin^2x

8sin^2 x -2sin x -1=0

8sin^2 x -4sin x +2sin x-1=0

4sin x(2sin x -1)+1(2sin x-1)=0

(4sin x +1)(2sin x-1)=0

Sin x=-1/4 ,sin x=1/2

x= .253, 2.889 ,x= pi/6,5pi/6