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Math Help - expression

  1. #1
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    expression

    Find an expression for :




    csc^2 (tan^-1 (3/x))


    in terms of x
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  2. #2
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    Quote Originally Posted by samtheman17 View Post
    Find an expression for :
    csc^2 (tan^-1 (3/x))
    in terms of x
    I think this is what the problem looks like?
    csc^2(Arctan(\frac{3}{x}))
    Arctan is just one way of writing the inverse tangent function.

    to solve this, let \theta=Arctan(\frac{3}{x}).
    Therefore, tan(\theta)=\frac{3}{x}
    and
    csc^2(Arctan(\frac{3}{x}))=csc^2(\theta)=1+cot^2(\  theta)=1+\frac{1}{tan^2(\theta)}
    So now you can write this in terms of
    tan(\theta)=\frac{3}{x}


    csc^2(Arctan(\frac{3}{x}))=1+\frac{1}{\frac{9}{x^2  }}=1+\frac{x^2}{9}
    Last edited by adkinsjr; October 24th 2009 at 02:05 PM.
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  3. #3
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    Note, I edited my original post because I messed up on the final line. So if you already looked at it, look again. It's fixed now. That should be the expression you're looking for.

    - BTW, this kind of question probably should have been posted in the trignometry section, since these are inverse trig functions.
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  4. #4
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    thank you! makes so much sense now
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