Question

Find all real numbers that satisfy the equation.

2 cos x + 1 = 0

Answer 1

2cosx = -1
cosx = -1/2
I know that cos 60° = cos π/6 = + 1/2
and the cosine is negative in quads II or III
x = 180-60 = 120° or x = 180+60 = 240°
or in radians
x = 2π/3 or x = 4π/3

the cosx function has a period of 360° or 2π radians, so
adding or subtracting 360° to any degree answer or adding/subtracting 2π to any radian answer will produce a new answer.