$\displaystyle \csc \theta = \frac{1}{\sin \theta}$ $\displaystyle \sec \theta = \frac{1}{\cos \theta}$ $\displaystyle \cot \theta = \frac{1}{\tan \theta}$
$\displaystyle \tan \theta = \frac{\sin \theta}{\cos \theta}$ $\displaystyle \cot \theta = \frac{\cos \theta}{\sin \theta}$
$\displaystyle \sin^2 \theta + \cos^2 \theta = 1$ $\displaystyle \tan^2 \theta + 1 = \sec^2 \theta$ $\displaystyle 1 + \cot^2 \theta = \csc^2 \theta$
$\displaystyle \frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C} = 2R$
제1 cos 법칙
$\displaystyle a = b \cos C + c \cos B$
$\displaystyle b = c \cos A + a \cos C$
$\displaystyle c = a \cos B + b \cos A$
제2 cos 법칙
$\displaystyle a^2 = b^2 + c^2 - 2bc \cos A$
$\displaystyle b^2 = c^2 + a^2 - 2ca \cos B$
$\displaystyle c^2 = a^2 + b^2 - 2ab \cos C$
① $\displaystyle \sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta$
② $\displaystyle \sin(\alpha - \beta) = \sin \alpha \cos \beta - \cos \alpha \sin \beta$
③ $\displaystyle \cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$
④ $\displaystyle \cos(\alpha - \beta) = \cos \alpha \cos \beta + \sin \alpha \sin \beta$
⑤ $\displaystyle \tan(\alpha + \beta) = \frac{\tan \alpha + \tan \beta}{1 - \tan \alpha \tan \beta}$
⑥ $\displaystyle \tan(\alpha - \beta) = \frac{\tan \alpha - \tan \beta}{1 + \tan \alpha \tan \beta}$
① $\displaystyle a \sin \theta + b \cos \theta = \sqrt{a^2 + b^2} \sin(\theta + \alpha)$
단, $\displaystyle \cos \alpha = \frac{a}{\sqrt{a^2 + b^2}}$, $\displaystyle \sin \alpha = \frac{b}{\sqrt{a^2 + b^2}}$ 또는 $\displaystyle \tan \alpha = \frac{b}{a}$
② $\displaystyle a \sin \theta + b \cos \theta = \sqrt{a^2 + b^2} \cos(\theta - \beta)$
단, $\displaystyle \cos \beta = \frac{b}{\sqrt{a^2 + b^2}}$, $\displaystyle \sin \beta = \frac{a}{\sqrt{a^2 + b^2}}$ 또는 $\displaystyle \tan \beta = \frac{a}{b}$
① $\displaystyle \sin 2\alpha = 2 \sin \alpha \cos \alpha$
② $\displaystyle \cos 2\alpha = \cos^2 \alpha - \sin^2 \alpha = 2 \cos^2 \alpha - 1 = 1 - 2 \sin^2 \alpha$
③ $\displaystyle \tan 2\alpha = \frac{2 \tan \alpha}{1 - \tan^2 \alpha}$
① $\displaystyle \sin 3\alpha = 3 \sin \alpha - 4 \sin^3 \alpha$
② $\displaystyle \cos 3\alpha = 4 \cos^3 \alpha - 3 \cos \alpha$
① $\displaystyle \sin^2 \frac{\alpha}{2} = \frac{1 - \cos \alpha}{2}$
② $\displaystyle \cos^2 \frac{\alpha}{2} = \frac{1 + \cos \alpha}{2}$
③ $\displaystyle \tan^2 \frac{\alpha}{2} = \frac{1 - \cos \alpha}{1 + \cos \alpha}$
① $\displaystyle \sin \alpha \cos \beta = \frac{1}{2} \{\sin(\alpha + \beta) + \sin(\alpha - \beta)\}$
② $\displaystyle \cos \alpha \sin \beta = \frac{1}{2} \{\sin(\alpha + \beta) - \sin(\alpha - \beta)\}$
③ $\displaystyle \cos \alpha \cos \beta = \frac{1}{2} \{\cos(\alpha + \beta) + \cos(\alpha - \beta)\}$
④ $\displaystyle \sin \alpha \sin \beta = -\frac{1}{2} \{\cos(\alpha + \beta) - \cos(\alpha - \beta)\}$
① $\displaystyle \sin \alpha + \sin \beta = 2 \sin \frac{\alpha + \beta}{2} \cos \frac{\alpha - \beta}{2}$
② $\displaystyle \sin \alpha - \sin \beta = 2 \cos \frac{\alpha + \beta}{2} \sin \frac{\alpha - \beta}{2}$
③ $\displaystyle \cos \alpha + \cos \beta = 2 \cos \frac{\alpha + \beta}{2} \cos \frac{\alpha - \beta}{2}$
④ $\displaystyle \cos \alpha - \cos \beta = -2 \sin \frac{\alpha + \beta}{2} \sin \frac{\alpha - \beta}{2}$