# Inverse reciprocal trigonometric function: finding the exact value

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##### Intros
###### Lessons
1. Introduction to Inverse Reciprocal Trigonometric Function: Finding the Exact Value
##### Examples
###### Lessons
1. Application of the Cancellation Laws

Solve the following inverse trigonometric functions:

1. $\sec^{-1} (\sec \frac{\pi}{3})$
2. $\cot (\cot^{-1} 5)$
3. $\csc (\csc^{-1} \frac{1}{2})$
2. Solving Expressions With One Inverse Trigonometry

Solve the following inverse trigonometric functions:

1. $\csc^{-1} \sqrt 2$
2. $\sec^{-1} \frac{1}{3}$
3. Evaluating Expressions With a Combination of Inverse and Non-Inverse Trigonometry

Solve the following inverse trigonometric functions:

1. $\sec (\cot^{-1} \frac{1}{\sqrt 3})$
2. $\cot (\sin^{-1} \frac{1}{3})$
3. $\csc (\arctan 3x)$
4. $\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})$
###### Topic Notes

$y = \csc x\;$ [$-\frac{\pi}{2}$, 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, $\infty$)

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