Explanation

3cos2x - sinx = 0
cos 2A = 1 – 2 sin\(^2\)A
3(1 - 2sin\(^2\)x) - sinx = 0
3 - 6sin\(^2\)x -sinx = 0
let sinx = p
3 - 6p\(^2\) -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\(^{-1}\) p
x = sin\(^{-1}\)(0.7953)
x = 52.68º

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

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