Solve :`cos x le - (1)/(2).`

Explanation

cos x is periodic with period `2 pi`.
So check the solution in `[0, 2pi].`

It is clear from the figure, that `cos x le -(1)/(2)` when `(2pi)/(3) le x le (4pi)/(3)`.
On generalizing the above solution,
`2npi + (2pi)/(3) le x le 2npi + (4pi)/(3) , n in Z`
So the solution to `cos x le -(1)/(2) rArr x in [2npi + (2pi)/(3), 2npi + (4pi)/(3)], n in Z`