Trig Identities and Equations

Pythagorean Identities

$\sin^2\theta + \cos^2\theta = 1$

$1 + \tan^2\theta = \sec^2\theta$

$1 + \cot^2\theta = \csc^2\theta$

Reciprocal Identities

$\csc\theta = \frac{1}{\sin\theta}$, $\sec\theta = \frac{1}{\cos\theta}$, $\cot\theta = \frac{1}{\tan\theta}$

Quotient Identities

$\tan\theta = \frac{\sin\theta}{\cos\theta}$, $\cot\theta = \frac{\cos\theta}{\sin\theta}$

$2\sin\theta - 1 = 0$ → $\sin\theta = \frac{1}{2}$ → $\theta = 30°, 150°$ (in $[0°, 360°]$).

$\cos^2\theta = \frac{3}{4}$ → $\cos\theta = \pm\frac{\sqrt{3}}{2}$ → $\theta = 30°, 150°, 210°, 330°$.