Solve for x, such that 0 <= pi < 2pi

Question

2cos(x/2) + √3 = 0

Answer 1

2cos(x/2) + √3 = 0

cos(x/2) = -√3/2

x/2=arccos(-√3/2)

x/2=±5π/6+2πk, k integer

x=±5π/3+4πk, k integer

You can separate a particular solution of your interest.

 

 

Answer 2

I think of x/2 as 60 degree that has been rotated one quarter turn clockwise.90degres =150 degrees, then divide by 2 and the answer is 75 degrees. The above answer is correct as expressed in radians

Answer 3

EDITED (because I answered as if you mentioned sine(x/2)...Bobosharif's answer looks good. The inequality that you wrote is true but of no use because it does not contain variable x.