# 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

$\sin(-u)=-\sin(u)$ $\cos(-u)=cos(u)$ $\tan(-u)=-\tan(u)$ $\csc(-u)=-\csc(u)$ $\sec(-u)=\sec(u)$ $\cot(-u)=-\cot(u)$ 