# Cofunction identities

### Cofunction identities

#### Lessons

Cofunction Identities: Basically, we need the sum of the left and right brackets to be 90° or $\frac{\pi}{2}$

$\sin(\frac{\pi}{2}-\theta)=\cos(\theta)$
$\sin(\theta)=\cos(\frac{\pi}{2}-\theta)$
$\tan(\frac{\pi}{2}-\theta)=\cot(\theta)$
$\tan(\theta)=\cot(\frac{\pi}{2}-\theta)$
$\sec(\frac{\pi}{2}-\theta)=\csc(\theta)$
$\sec(\theta)=\csc(\frac{\pi}{2}-\theta)$
• Introduction
What are cofunction identities?
• Relationships between trigonometric functions and their cofunctions

• 1.
Write the following in terms of its cofunction:

$\blacksquare$ $\sin(23)$
$\blacksquare$ $\cos(47)$
$\blacksquare$ $\tan(\frac{\pi}{6})$
$\blacksquare$ $\csc(\frac{\pi}{6})$

• 2.
Solve for $x$
a)
$\sin(x-\frac{\pi}{4})=\cos(\frac{\pi}{12}+3x)$

b)
$\cot(8^{\circ}+x)=\tan(4x-3^{\circ})$

c)
$\csc(3x+\frac{\pi}{5})=\sec(2x-\frac{\pi}{10})$