Inverse reciprocal trigonometric function: finding the exact value

Inverse reciprocal trigonometric function: finding the exact value

Lessons

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

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

y=cotxy = \cot x\; (0, π\pi)

y=csc1xy = \csc^{-1} x\; (-\infty, -1] \cup [1, \infty)

y=sec1xy = \sec^{-1} x\; (-\infty, -1] \cup [1, \infty)

y=cot1xy = \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)
    sec1(secπ3)\sec^{-1} (\sec \frac{\pi}{3})

    b)
    cot(cot15)\cot (\cot^{-1} 5)

    c)
    csc(csc112)\csc (\csc^{-1} \frac{1}{2})


  • 3.
    Solving Expressions With One Inverse Trigonometry

    Solve the following inverse trigonometric functions:

    a)
    csc12\csc^{-1} \sqrt 2

    b)
    sec113\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(cot113)\sec (\cot^{-1} \frac{1}{\sqrt 3})

    b)
    cot(sin113)\cot (\sin^{-1} \frac{1}{3})

    c)
    csc(arctan3x)\csc (\arctan 3x)

    d)
    csc(cos1xx2+16)\csc (\cos^{-1} \frac{x}{\sqrt{x^{2} + 16}})