Solve 3cos2x - sinx = 0 for 0º≤x≤360º

Answer Details

3cos2x - sinx = 0
cos 2A = 1 – 2 sin2 ${}^2$A
3(1 - 2sin2 ${}^2$x) - sinx = 0
3 - 6sin2 ${}^2$x -sinx = 0
let sinx = p
3 - 6p2 ${}^2$ -p = 0
-6p2 - p +3 = 0

factors of p in the eqn: 

p = 0.7953 or 0.6287
when p = 0.7953
p = sinx
x = sin−1 ${}^{-1}$ p
x = sin−1 ${}^{-1}$(0.7953)
x = 52.68º

when p = 0.6287
p = sinx
x = sin−1 ${}^{-1}$ p
x = sin−1 ${}^{-1}$(0.6287)
x = 38.95º