Inverse reciprocal trigonometric function: finding the exact value

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

    Solve the following inverse trigonometric functions:

    1. sec⁡−1(sec⁡π3)\sec^{-1} (\sec \frac{\pi}{3})
    2. cot⁡(cot⁡−15)\cot (\cot^{-1} 5)
    3. csc⁡(csc⁡−112)\csc (\csc^{-1} \frac{1}{2})
  2. Solving Expressions With One Inverse Trigonometry

    Solve the following inverse trigonometric functions:

    1. csc⁡−12\csc^{-1} \sqrt 2
    2. sec⁡−113\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⁡−113)\sec (\cot^{-1} \frac{1}{\sqrt 3})
    2. cot⁡(sin⁡−113)\cot (\sin^{-1} \frac{1}{3})
    3. csc⁡(arctan⁡3x)\csc (\arctan 3x)
    4. csc⁡(cos⁡−1xx2+16)\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})
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Topic Notes

y=csc⁡x  y = \csc x\; [−π2-\frac{\pi}{2}, 0) ∪\cup (0, π2\frac{\pi}{2}]

y=sec⁡x  y = \sec x\; [0, π2\frac{\pi}{2}) ∪\cup (π2,π\frac{\pi}{2}, \pi]

y=cot⁡x  y = \cot x\; (0, π\pi)

y=csc⁡−1x  y = \csc^{-1} x\; (-∞\infty, -1] ∪\cup [1, ∞\infty)

y=sec⁡−1x  y = \sec^{-1} x\; (-∞\infty, -1] ∪\cup [1, ∞\infty)

y=cot⁡−1x  y = \cot^{-1} x\; (-∞,∞\infty, \infty)

Basic Concepts