# High School Trigonometry/Fundamental Identities

Jump to: navigation, search

## Contents

### Reciprocal Identities

${\displaystyle \sin u=\left({\frac {1}{\csc u}}\right)}$

${\displaystyle \cos u=\left({\frac {1}{\sec u}}\right)}$

${\displaystyle \tan u=\left({\frac {1}{\ cotu}}\right)}$

${\displaystyle \csc u=\left({\frac {1}{\sin u}}\right)}$

${\displaystyle \sec u=\left({\frac {1}{\cos u}}\right)}$

${\displaystyle \cot u=\left({\frac {1}{\tan u}}\right)}$

### Pythagorean Identities

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

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

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

### Quotient Identities

${\displaystyle \tan u=\left({\frac {\sin u}{\cos u}}\right)}$

${\displaystyle \cot u=\left({\frac {\cos u}{\sin u}}\right)}$

### Co-Function Identities

${\displaystyle \sin(\left({\frac {\pi }{2}}\right)-u)=\cos u}$

${\displaystyle \cos(\left({\frac {\pi }{2}}\right)-u)=\sin u}$

${\displaystyle \tan(\left({\frac {\pi }{2}}\right)-u)=\cot u}$

${\displaystyle \csc(\left({\frac {\pi }{2}}\right)-u)=\sec u}$

${\displaystyle \sec(\left({\frac {\pi }{2}}\right)-u)=\csc u}$

${\displaystyle \cot(\left({\frac {\pi }{2}}\right)-u)=\tan u}$

### Even-Odd Identities

${\displaystyle \sin(-u)=-\sin(u)}$

${\displaystyle \cos(-u)=cos(u)}$

${\displaystyle \tan(-u)=-\tan(u)}$

${\displaystyle \csc(-u)=-\csc(u)}$

${\displaystyle \sec(-u)=\sec(u)}$

${\displaystyle \cot(-u)=-\cot(u)}$

This material was adapted from the original CK-12 book that can be found here. This work is licensed under the Creative Commons Attribution-Share Alike 3.0 United States License