High School Trigonometry/Fundamental Identities

Reciprocal Identities

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

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

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

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

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

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

Pythagorean Identities

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

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

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

Quotient Identities

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

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

Co-Function Identities

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

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

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

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

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

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

Even-Odd Identities

$\sin (-u)=-\sin (u)$

$\cos (-u)=cos(u)$

$\tan (-u)=-\tan (u)$

$\csc (-u)=-\csc (u)$

$\sec (-u)=\sec (u)$

$\cot (-u)=-\cot (u)$