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Math Help - inverse trig functions

  1. #1
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    [solved] inverse trig functions

    let x be a positive number and let theta= tan^-1 x

    a) simplify tan ( pi/2 - theta)
    b) show that tan^-1 (1/x) = (pi/2) - theta

    Thanks

    Do i have to expand the tan function?

    Nvm i got it. Its just a complimentary angle. so cot theta.
    Last edited by deltaxray; August 28th 2010 at 05:41 AM.
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  2. #2
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    \tan{\theta} = x.


    \tan{\left(\frac{\pi}{2} - \theta\right)} = \frac{\sin{\left(\frac{\pi}{2} - \theta\right)}}{\cos{\left(\frac{\pi}{2} - \theta\right)}}

     = \frac{\cos{\theta}}{\sin{\theta}}

     = \frac{1}{\tan{\theta}}

     = \frac{1}{x}.


    And since \tan{\left(\frac{\pi}{2} - \theta\right)} = \frac{1}{x}

    that means \tan^{-1}\left(\frac{1}{x}\right) = \frac{\pi}{2} - \theta.
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