图解三角函数公式

图解三角函数公式

前情概要

三角公式的图形表示

v2-594523cca2cda4dcad8dca1b966f2b33_1440w

https://www.desmos.com/calculator/3tdwbb9vcm

https://www.desmos.com/calculator/klyuz0h2ty

https://www.desmos.com/calculator/eqbdiderwj

图形解释

平方关系: \(\sin^2\theta+\cos^2\theta=1\)\(\tan^2\theta+1=\sec^2\theta\)\(\cot^2\theta+1=\csc^2\theta\)

倒数关系: \(\tan\theta=\cfrac{1}{\cot\theta}\)\(\sec\theta=\cfrac{1}{\cos\theta}\)\(\csc\theta=\cfrac{1}{\sin\theta}\)

\(\sin(\cfrac{\pi}{2}-\theta)=\cos\theta\)\(\cos(\cfrac{\pi}{2}-\theta)=\sin\theta\)

等面积 \(\sin\theta\cdot\sec\theta=\tan\theta\)