Question

How do you solve `cos(1/2x)=-sqrt3/2`?

Answer 1

`x = 5/3pi+4pi`

or

`x = -5/3pi+4pi`

Explanation:

Since it's a known fact that the cosine equals `-sqrt(3)/2` for an angle of `\pm 5/6 pi`, we knot that the argument of the function must be one of the two angles.

In this case, the argument is `x/2`, so we have

`x/2 = 5/6pi+2pi`

or

`x/2 = -5/6pi+2pi`

These solutions lead to

`x = 5/3pi+4pi`

or

`x = -5/3pi+4pi`