# 同界角

45度的3個同界角

## 性質

1. 若有兩個角有相同的始與終邊，則兩個角互為同界角
2. 若兩角相差360度的整數倍則兩個角互為同界角

${\displaystyle \theta _{1}-\theta _{2}=360^{\circ }k,\,k\in \mathbb {Z} }$

${\displaystyle \theta _{1}-\theta _{2}=2k\pi ,\,k\in \mathbb {Z} }$

${\displaystyle \sin \theta _{1}-\sin \theta _{2}=0}$
${\displaystyle \cos \theta _{1}-\cos \theta _{2}=0}$

## 與三角函數關係

${\displaystyle \tan }$ ${\displaystyle \cot }$  的周期

${\displaystyle \sin }$ ${\displaystyle \cos }$ ${\displaystyle \csc }$ ${\displaystyle \sec }$  的周期
{\displaystyle {\begin{aligned}\sin(\theta +{\tfrac {\pi }{2}})&=+\cos \theta \\\cos(\theta +{\tfrac {\pi }{2}})&=-\sin \theta \\\tan(\theta +{\tfrac {\pi }{2}})&=-\cot \theta \\\cot(\theta +{\tfrac {\pi }{2}})&=-\tan \theta \\\sec(\theta +{\tfrac {\pi }{2}})&=-\csc \theta \\\csc(\theta +{\tfrac {\pi }{2}})&=+\sec \theta \end{aligned}}}  {\displaystyle {\begin{aligned}\sin(\theta +\pi )&=-\sin \theta \\\cos(\theta +\pi )&=-\cos \theta \\\tan(\theta +\pi )&=+\tan \theta \\\cot(\theta +\pi )&=+\cot \theta \\\sec(\theta +\pi )&=-\sec \theta \\\csc(\theta +\pi )&=-\csc \theta \end{aligned}}}  {\displaystyle {\begin{aligned}\sin(\theta +2\pi )&=+\sin \theta \\\cos(\theta +2\pi )&=+\cos \theta \\\tan(\theta +2\pi )&=+\tan \theta \\\cot(\theta +2\pi )&=+\cot \theta \\\sec(\theta +2\pi )&=+\sec \theta \\\csc(\theta +2\pi )&=+\csc \theta \end{aligned}}}

## 參考文獻

1. ^ Neal, Karla V.; R. David Gustafson, Jeffrey D. Hughes. Coterminal angles. Precalculus, 1st ed.. Cengage Learning. : 第412頁. ISBN 1133712673. （原始内容存档于2019-10-18）.
2. ^ Slavin, Steve; Ginny Crisonino. Circle. Wiley Self-Teaching Guides第 155 卷. John Wiley & Sons. 2004-10-28: 第90頁. ISBN 0471680192. （原始内容存档于2019-11-06）.