$\cos^2 x + \sin^2 x = 1$
- $\cos^2 x = 1 - \sin^2 x$
- $\sin^2 x = 1 - \cos^2 x$
$\sec^2 x - \tan^2 x = 1$
- $\sec^2 x = 1 + \tan^2 x$
- $\tan^2 x = \sec^2 x - 1$
$\csc^2 x - \cot^2 x = 1$
- $\csc^2 x = 1 + \cot^2 x$
- $\cot^2 x = \csc^2 x - 1$

The sign of trigonometric functions depends on the quadrant.

Hint for memory: All Students Take Coffee (ASTC Rule)

Angle	$0^\circ$	$30^\circ$	$45^\circ$	$60^\circ$	$90^\circ$
$\sin \theta$	$0$	$\frac{1}{2}$	$\frac{1}{\sqrt{2}}$	$\frac{\sqrt{3}}{2}$	$1$
$\cos \theta$	$1$	$\frac{\sqrt{3}}{2}$	$\frac{1}{\sqrt{2}}$	$\frac{1}{2}$	$0$
$\tan \theta$	$0$	$\frac{1}{\sqrt{3}}$	$1$	$\sqrt{3}$	Undefined