Inverse reciprocal trigonometric function: finding the exact value

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Introduction to Inverse Reciprocal Trigonometric Function: Finding the Exact Value

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Application of the Cancellation Laws
Solve the following inverse trigonometric functions:
1. $\sec^{-1} (\sec \frac{\pi}{3})$
2. $\cot (\cot^{-1} 5)$
3. $\csc (\csc^{-1} \frac{1}{2})$
Solving Expressions With One Inverse Trigonometry
Solve the following inverse trigonometric functions:
1. $\csc^{-1} \sqrt 2$
2. $\sec^{-1} \frac{1}{3}$
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. $\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})$

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

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