单位圆
Snipaste_2022-08-06_18-19-32.png
弧度制
Snipaste_2022-08-06_18-20-20.png
三角函数
Snipaste_2022-08-06_18-36-25.png
$$\sin (x) = {对边 \over 斜边} , \cos (x) = {邻边 \over 斜边} , \tan (x) = {对边 \over 斜边}$$
$$\csc (x) = {1 \over \sin (x)} , \sec = {1 \over \cos (x) } , \cot (x) = {1 \over \tan (x)}$$

常用三角函数值

0$${\pi \over 6}$$$${\pi \over 4}$$$${\pi \over 3}$$$${\pi \over 2}$$
$$\sin$$$$0$$$${1 \over 2}$$$$1 \over \sqrt{2}$$$$\sqrt{3} \over 2$$$$1$$
$$\cos$$$$1$$$$\sqrt{3} \over 2$$$$1 \over \sqrt{2}$$$${1 \over 2}$$$$0$$
$$\tan$$$$0$$$$1 \over \sqrt{3}$$$$1$$$$\sqrt{3}$$$$*$$

ASTC
Snipaste_2022-08-06_18-56-58.png

奇偶性
$$\sin(-x) = -\sin(x) , \tan(-x) = -\tan(x) , \cos(-x) = \cos(x)$$

三角恒等式
$$\tan(x) = {\sin(x) \over \cos(x)} , \cot(x) = {\cos(x) \over \sin(x)}$$

毕达哥拉斯定理
$$\sin^{2}(x) + \cos^{2}(x) = 1$$
$$1 + \tan^{2}(x) = \sec^{2}(x)$$
$$1 + \cot^{2}(x) = \csc^{2}(x)$$

两角和
$$\sin(A+B)= \sin(A)\cdot\cos(B) + \cos(A)\cdot\sin(B) , \sin(A-B)= \sin(A)\cdot\cos(B) - \cos(A)\cdot\sin(B)$$
$$\cos(A+B)= \cos(A)\cdot\cos(B) - \sin(A)\cdot\sin(B) , \cos(A-B)= \cos(A)\cdot\cos(B) + \sin(A)\cdot\sin(B)$$

倍角公式
$$\sin(2x) = 2\sin(x)\cos(x)$$
$$\cos(2x) = cos^{2}(x) - sin^{2}(x) = 2\cos^{2}(x) - 1 = 1 - 2\sin^{2}(x)$$