Solve 3cos2x - sinx = 0 for 0º≤x≤360º

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