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Math Help - Solving for Variable in an Inverse function

  1. #1
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    Solving for Variable in an Inverse function

    I am doing this problem and I have to solve for variable v.

    -2kt = sin-1(v/k)


    the answer is supposedly, v = k sin (-2*k*t)


    Please show me the steps. Thank you.
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  2. #2
    Super Member Aryth's Avatar
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    You are given:

    -2kt = \sin^{-1}{\left(\frac{v}{k}\right)}

    The only real issue here is the inverse sin, but recall the identity:

    \sin{(\sin^{-1}{(x)})} = x

    So, if we take the sine of both sides we get:

    \sin{(-2kt)} = \sin{\left(\sin^{-1}{\left(\frac{v}{k}\right)}\right)}

    \sin{(-2kt)} = \frac{v}{k}

    Now we multiply both sides by k and get:

    k\sin{(-2kt)} = v

    And there you go.
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