Trigonometric inequalities

A trigonometric inequality is an inequality that involves trigonometric functions such as $\sin x$, $\cos x$, or $\tan x$. To solve these, we find all values of $x$ (usually in a given interval) that make the inequality true.

Important properties

• Trigonometric functions are periodic, so solutions often repeat at regular intervals.

• The range of $\sin x$ and $\cos x$ is $[-1, 1]$, which limits possible solutions.

• Inequalities may require considering the sign of the trigonometric function in different intervals.

• Graphical methods can help visualize where the inequality holds.