# Inverse reciprocal trigonometric function: finding the exact value

### Inverse reciprocal trigonometric function: finding the exact value

#### Lessons

$y = \csc x\;$ [$-\frac{\pi}{2}$, 0) $\cup$ (0, $\frac{\pi}{2}$]

$y = \sec x\;$ [0, $\frac{\pi}{2}$) $\cup$ ($\frac{\pi}{2}, \pi$]

$y = \cot x\;$ (0, $\pi$)

$y = \csc^{-1} x\;$ (-$\infty$, -1] $\cup$ [1, $\infty$)

$y = \sec^{-1} x\;$ (-$\infty$, -1] $\cup$ [1, $\infty$)

$y = \cot^{-1} x\;$ (-$\infty, \infty$)

• 1.
Introduction to Inverse Reciprocal Trigonometric Function: Finding the Exact Value

• 2.
Application of the Cancellation Laws

Solve the following inverse trigonometric functions:

a)
$\sec^{-1} (\sec \frac{\pi}{3})$

b)
$\cot (\cot^{-1} 5)$

c)
$\csc (\csc^{-1} \frac{1}{2})$

• 3.
Solving Expressions With One Inverse Trigonometry

Solve the following inverse trigonometric functions:

a)
$\csc^{-1} \sqrt 2$

b)
$\sec^{-1} \frac{1}{3}$

• 4.
Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry

Solve the following inverse trigonometric functions:

a)
$\sec (\cot^{-1} \frac{1}{\sqrt 3})$

b)
$\cot (\sin^{-1} \frac{1}{3})$

c)
$\csc (\arctan 3x)$

d)
$\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})$