基本恒等式

1. $\sin^2 x + \cos^2 x = 1$
2. $1 + \tan^2 x = \sec^2 x$
3. $1 + \cot^2 x = \csc^2 x$

和角公式

1. $\sin(x + y) = \sin x \cos y + \cos x \sin y$
2. $\sin(x - y) = \sin x \cos y - \cos x \sin y$
3. $\cos(x + y) = \cos x \cos y - \sin x \sin y$
4. $\cos(x - y) = \cos x \cos y + \sin x \sin y$
5. $\tan(x + y) = \frac{\tan x + \tan y}{1 - \tan x \tan y}$
6. $\tan(x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}$

倍角公式

1. $\sin 2x = 2\sin x \cos x$
2. $\cos 2x = \cos^2 x - \sin^2 x = 2\cos^2 x - 1 = 1 - 2\sin^2 x$
3. $\tan 2x = \frac{2\tan x}{1 - \tan^2 x}$

半角公式

1. $\sin^2 x = \frac{1 - \cos 2x}{2}$
2. $\cos^2 x = \frac{1 + \cos 2x}{2}$
3. $\tan^2 x = \frac{1 - \cos 2x}{1 + \cos 2x}$

积化和差

1. $\sin x \sin y = \frac{1}{2}[\cos(x - y) - \cos(x + y)]$
2. $\cos x \cos y = \frac{1}{2}[\cos(x - y) + \cos(x + y)]$
3. $\sin x \cos y = \frac{1}{2}[\sin(x + y) + \sin(x - y)]$

和差化积

1. $\sin x + \sin y = 2 \sin\left(\frac{x + y}{2}\right) \cos\left(\frac{x - y}{2}\right)$
2. $\sin x - \sin y = 2 \cos\left(\frac{x + y}{2}\right) \sin\left(\frac{x - y}{2}\right)$
3. $\cos x + \cos y = 2 \cos\left(\frac{x + y}{2}\right) \cos\left(\frac{x - y}{2}\right)$
4. $\cos x - \cos y = -2 \sin\left(\frac{x + y}{2}\right) \sin\left(\frac{x - y}{2}\right)$

特殊角的三角函数值

1. $\sin 0 = 0, \cos 0 = 1, \tan 0 = 0$
2. $\sin \frac{\pi}{6} = \frac{1}{2}, \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}, \tan \frac{\pi}{6} = \frac{1}{\sqrt{3}}$
3. $\sin \frac{\pi}{4} = \frac{\sqrt{2}}{2}, \cos \frac{\pi}{4} = \frac{\sqrt{2}}{2}, \tan \frac{\pi}{4} = 1$
4. $\sin \frac{\pi}{3} = \frac{\sqrt{3}}{2}, \cos \frac{\pi}{3} = \frac{1}{2}, \tan \frac{\pi}{3} = \sqrt{3}$
5. $\sin \frac{\pi}{2} = 1, \cos \frac{\pi}{2} = 0, \tan \frac{\pi}{2}$ is undefined