The equation cosx=12 has the solution x=3 in the first quadrant, and the symmetric solution x=2−3=53 in the fourth quadrant.
Angle 3 Angle 53
If we add multiples of 2 to these two solutions, we obtain all the solutions
x=3+2n and x=53+2n
where n is an arbitrary integer.
2
3−3=53
333+2n3+2n