Algebra and Trigonometry, 5th Edition

7.2 Identities: Cofunction, Double-Angle, and Half-Angle

• Use cofunction identities to derive other identities.

• Use the double-angle identities to find function values of twice an angle when one function value is known for that angle.

• Use the half-angle identities to find function values of half an angle when one function value is known for that angle.

• Simplify trigonometric expressions using the double-angle identities and the half-angle identities.

Cofunction Identities

Each of the identities listed below yields a conversion to a cofunction. For this reason, we call them cofunction identities.

Cofunction Identities

$$\begin{array}{cc}\sin \left({\displaystyle \frac{\pi }{2}}-x\right)=\cos x,& \cos \left({\displaystyle \frac{\pi }{2}}-x\right)=\sin x,\\ \tan \left({\displaystyle \frac{\pi }{2}}-x\right)=\cot x,& \cot \left({\displaystyle \frac{\pi }{2}}-x\right)=\tan x,\\ \sec \left({\displaystyle \frac{\pi }{2}}-x\right)=\csc x,& \csc \left({\displaystyle \frac{\pi }{2}}-x\right)=\sec x,\end{array}$$

We verified the ...