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Math Help - Help evaluating this trig expression!

  1. #1
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    Help evaluating this trig expression!

    sec(tan^{-1} 2x)

    I think the 2x has something to do with why I can't solve this problem, but even then, I still don't remember what to do about it...
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by orkdork View Post
    sec(tan^{-1} 2x)

    I think the 2x has something to do with why I can't solve this problem, but even then, I still don't remember what to do about it...
    Create a right triangle that satisfies \tan\theta=2x. Then find \sec\theta using the triangle constructed.

    Can you proceed?
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  3. #3
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    I think I get it, i'll try it
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  4. #4
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    Ok, yeah, I don't know how to find the right triangle... ._.
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by orkdork View Post
    Ok, yeah, I don't know how to find the right triangle... ._.
    Recall \tan\theta=\dfrac{\text{opp}}{\text{adj}}. So in the case of \tan\theta=2x, 2x is the side opposite of \theta, and 1 is the side adjacent to \theta.

    As a result, the hypotenuse of the triangle is \sqrt{1+4x^2} (verify).

    Now what is \sec\theta?
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  6. #6
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    ohh...ok that makes sense now thanks
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