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
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Examples
Lessons
  1. Application of the Cancellation Laws

    Solve the following inverse trigonometric functions:

    1. secโกโˆ’1(secโกฯ€3)\sec^{-1} (\sec \frac{\pi}{3})
    2. cotโก(cotโกโˆ’15)\cot (\cot^{-1} 5)
    3. cscโก(cscโกโˆ’112)\csc (\csc^{-1} \frac{1}{2})
  2. Solving Expressions With One Inverse Trigonometry

    Solve the following inverse trigonometric functions:

    1. cscโกโˆ’12\csc^{-1} \sqrt 2
    2. secโกโˆ’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. secโก(cotโกโˆ’113)\sec (\cot^{-1} \frac{1}{\sqrt 3})
    2. cotโก(sinโกโˆ’113)\cot (\sin^{-1} \frac{1}{3})
    3. cscโก(arctanโก3x)\csc (\arctan 3x)
    4. cscโก(cosโกโˆ’1xx2+16)\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})
Topic Notes
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y=cscโกxโ€…โ€Šy = \csc x\; [โˆ’ฯ€2-\frac{\pi}{2}, 0) โˆช\cup (0, ฯ€2\frac{\pi}{2}]

y=secโกxโ€…โ€Šy = \sec x\; [0, ฯ€2\frac{\pi}{2}) โˆช\cup (ฯ€2,ฯ€\frac{\pi}{2}, \pi]

y=cotโกxโ€…โ€Šy = \cot x\; (0, ฯ€\pi)

y=cscโกโˆ’1xโ€…โ€Šy = \csc^{-1} x\; (-โˆž\infty, -1] โˆช\cup [1, โˆž\infty)

y=secโกโˆ’1xโ€…โ€Šy = \sec^{-1} x\; (-โˆž\infty, -1] โˆช\cup [1, โˆž\infty)

y=cotโกโˆ’1xโ€…โ€Šy = \cot^{-1} x\; (-โˆž,โˆž\infty, \infty)