2 cos2 x + 7 sin x =5

Question

I am trying rearrange my equation and I can not seem to get it. Please help. it is in interval [0, 360) degrees 

Answer 1

2 cos2x + 7sin x = 5

2(cos² x - sin² x) + 7sin x = 5

2cos² x - 2sin² x + 7sin x = 5

2(1 - sin² x) - 2sin² x + 7sin x = 5

2 - 2sin² x - 2sin² x + 7sin x = 5

2 - 4sin² x + 7sin x = 5

0 = 4sin² x - 7x + 3

0 = (sin x - 1)(4sin x - 3)

 

sin x = 1

sin^-1 1 = x

π/2 = x

 

OR

 

4sin x - 3 = 0

sin x = 3/4

sin^-1 0.75 = x

48.59° = x