Angles in All Four Quadrants

Measuring anticlockwise from the positive $x$-axis, angles fall into four quadrants: $0^{\circ }$–$90^{\circ }$, $90^{\circ }$–$180^{\circ }$, $180^{\circ }$–$270^{\circ }$ and $270^{\circ }$–$360^{\circ }$. Each quadrant decides whether $\sin$, $\cos$ and $\tan$ come out positive or negative.

CAST records which ratios are positive in each quadrant, read anticlockwise from the 4th: $\text{C}$ (4th: only $\cos$), $\text{A}$ (1st: $\text{a}$ll), $\text{S}$ (2nd: only $\sin$), $\text{T}$ (3rd: only $\tan$).

For any angle, the $\text{related acute angle}$ is its distance to the nearest part of the $x$-axis. The size of the trig ratio matches that acute angle; the CAST diagram supplies the sign.