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Math Help - [SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

  1. #1
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    [SOLVED] How to calculate integral of sqrt( 2 - 2cos(t) ) ?

    I want to evaluate the integral of this, but I am having some difficulty simplyfing the expresion to integrate. \sqrt{2 - 2\cos t}  = \sqrt{2} \sqrt{1-\cos t} and I don't know what else to do...

    Any help is appreciated.

    Thanks.
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  2. #2
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    \cos t=1-2\sin ^{2}\frac{t}{2}.
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  3. #3
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    Quote Originally Posted by Krizalid View Post
    \cos t=1-2\sin ^{2}\frac{t}{2}.
    Thanks for your reply. That does work. But, may I ask how did you know that? Certainly there's a way do deduce that expression.

    Thanks.
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  4. #4
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    Of course, just consider the double angle formula for the cosine, then \cos2t=1-2\sin^2t, then i just put t\mapsto\frac t2.
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  5. #5
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    Quote Originally Posted by Krizalid View Post
    Of course, just consider the double angle formula for the cosine, then \cos2t=1-2\sin^2t, then i just put t\mapsto\frac t2.
    I have never used that trigonometric identity before, but now am aware of it. Thanks for your help.

    Cheers.
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