High School Trigonometry/Fundamental Identities

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Reciprocal Identities[edit]

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

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

\tan u=\left(\frac{1}{\ cot u} \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[edit]

\sin^2 u + \cos^2 u=1

1+\tan^2 u=\sec^2

1+\cot^2 u=\csc^2 u

Quotient Identities[edit]

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

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

Co-Function Identities[edit]

\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[edit]

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

\cos (-u)=cos (u)

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

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

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

\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