Solve for all angles between 0 and 360: 2cos^2(x)+cos(X)=1

Question

Solve for all angles between 0 and 360: 2cos^2(x)+cos(X)=1

Answer 1

2cos²x + cosx - 1 = 0

 

(2cosx - 1)(cosx + 1) = 0

 

2cosx - 1 = 0 or cosx + 1 = 0

 

cosx = 1/2 or cosx = -1

 

If cosx = -1, then x = 180°

 

If cosx = 1/2, then x = 60° or 300°

 

Solutions between 0° and 360°:  60°, 180°, 300°