# 三角函數公式一覽

(由三角函數公式大全跳轉過嚟)

## 單位圓定義

${\displaystyle \sin \theta ={\frac {y}{r}}}$

${\displaystyle \cos \theta ={\frac {x}{r}}}$

${\displaystyle \tan \theta ={\frac {y}{x}}}$

${\displaystyle \sec \theta ={\frac {r}{x}}}$

${\displaystyle \csc \theta ={\frac {r}{y}}}$

${\displaystyle \cot \theta ={\frac {x}{y}}}$

## 相互關係

${\displaystyle \csc \theta ={\frac {1}{\sin \theta }}}$

${\displaystyle \sec \theta ={\frac {1}{\cos \theta }}}$

${\displaystyle \cot \theta ={\frac {1}{\tan \theta }}}$

${\displaystyle \tan \theta ={\frac {\sin \theta }{\cos \theta }}={\frac {\sec \theta }{\csc \theta }}}$

${\displaystyle \cot \theta ={\frac {\cos \theta }{\sin \theta }}={\frac {\csc \theta }{\sec \theta }}}$

${\displaystyle \sin ^{2}\theta +\cos ^{2}\theta =1}$

${\displaystyle 1+\tan ^{2}\theta =\sec ^{2}\theta }$

${\displaystyle 1+\cot ^{2}\theta =\csc ^{2}\theta }$

## 移相公式

${\displaystyle \sin(x+2n\pi )=\sin(x)\quad \forall n\in \mathbb {Z} }$

${\displaystyle \cos(x+2n\pi )=\cos(x)\quad \forall n\in \mathbb {Z} }$

${\displaystyle \tan(x+n\pi )=\tan(x)\quad \forall n\in \mathbb {Z} }$

${\displaystyle \sec(x+2n\pi )=\sec(x)\quad \forall n\in \mathbb {Z} }$

${\displaystyle \csc(x+2n\pi )=\csc(x)\quad \forall n\in \mathbb {Z} }$

${\displaystyle \cot(x+n\pi )=\cot(x)\quad \forall n\in \mathbb {Z} }$

${\displaystyle \sin(x+\pi )=-\sin(x)}$

${\displaystyle \cos(x+\pi )=-\cos(x)}$

${\displaystyle \sec(x+\pi )=-\sec(x)}$

${\displaystyle \csc(x+\pi )=-\csc(x)}$

${\displaystyle \sin(\pi -x)=\sin(x)}$

${\displaystyle \cos(\pi -x)=-\cos(x)}$

${\displaystyle \tan(\pi -x)=-\tan(x)}$

${\displaystyle \sec(\pi -x)=-\sec(x)}$

${\displaystyle \csc(\pi -x)=\csc(x)}$

${\displaystyle \cot(\pi -x)=-\cot(x)}$