precllac math problem 4

Question

Solve the equation for exact solutions over the interval​ [0, 2π​).

−2sin²x=3sinx+1

Answer 1

-2sin^2(x) = 3sinx +1

2sin^2(x) + 3sinx +1 = 0

let sinx = y

2y^2 +3y +1 = 0

(2y +1)(y+1) = 0

y =-1 = sinx

x = 270 degrees

y = -1/2= sinx

x = 210 or 330 degrees

three solutions

x= 210, 270 or 330 degrees