# Trigonometric Inequalities

We will consider here the simplest trigonometric inequality of the form f(x)<a (or f(x)>a), where f(x) is some trigonometric function.

Example. Solve $cos(x)<0.5$.

Let's draw graph of the function $y=cos(x)$ and draw line $y=0.5$. We are interested in those intervals where cosine is below line y=0.5. One of such intervals is $(pi/3,(5pi)/3)$. Using periodicity of cosine we obtain solution: $pi/3+2pik<x<(5pi)/3+2pik,k in Z$.