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Math Help - Trigonometry Help [Q1]

  1. #1
    Member looi76's Avatar
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    Trigonometry Help [Q1]

    Question:
    Given x = \arcsin \frac{1}{3} , find the exact value of:
    a. \cos x
    b. \tan x
    c. \cot x
    d. \sec x
    e. \csc x

    Attempt:

    a. \cos x

    = \cos (x = \arcsin \frac{1}{3})

    = 0.942809041

    \color{red}{= 2 \frac{\sqrt{2}}{3}}

    How can I get the fraction answer?
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  2. #2
    Banned
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    Quote Originally Posted by looi76 View Post
    Question:
    Given x = \arcsin \frac{1}{3} , find the exact value of:
    a. \cos x
    b. \tan x
    c. \cot x
    d. \sec x
    e. \csc x

    Attempt:

    a. \cos x

    = \cos (x = \arcsin \frac{1}{3})

    = 0.942809041

    \color{red}{= 2 \frac{\sqrt{2}}{3}}

    How can I get the fraction answer?
    x= \sin^{-1}\left(\frac{1}{3}\right)

    \Rightarrow \sin x =\frac{1}{3}

    \cos x = \sqrt{1-\sin^2 x}=\sqrt{1-\left(\frac{1}{3}\right)^2 }=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}

    \tan x = \frac{\sin x}{\cos x}=\frac{.......}{.......} finish it.

    \cot x = \frac{1}{\tan x}=\frac{1}{.......} finish it.

    \sec x = \frac{1}{\cos x}=\frac{1}{.......} finish it.

    \csc x = \frac{1}{\sin x}=\frac{1}{.......} finish it.

    got it ???
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by Shyam View Post
    x= \sin^{-1}\left(\frac{1}{3}\right)

    \Rightarrow \sin x =\frac{1}{3}

    \cos x = \sqrt{1-\sin^2 x}=\sqrt{1-\left(\frac{1}{3}\right)^2 }=\sqrt{\frac{8}{9}}=\frac{2\sqrt{2}}{3}

    \tan x = \frac{\sin x}{\cos x}=\frac{.......}{.......} finish it.

    \cot x = \frac{1}{\tan x}=\frac{1}{.......} finish it.

    \sec x = \frac{1}{\cos x}=\frac{1}{.......} finish it.

    \csc x = \frac{1}{\sin x}=\frac{1}{.......} finish it.

    got it ???
    \cos x = \pm \sqrt{1-\sin^2 x}=\pm \sqrt{1-\left(\frac{1}{3}\right)^2 }=\pm \sqrt{\frac{8}{9}}=\pm \frac{2\sqrt{2}}{3}

    CB
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