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Math Help - Reducing fractions with pi in them

  1. #1
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    Reducing fractions with pi in them

    I am trying to simplify the expression

    \cos\frac{35\pi}{4}+i\sin\frac{35\pi}{4}

    The cosine and sine functions can be reduced modulo 2\pi, right? So I wrote this as

    \cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4}

    after subtracting \frac{32\pi}{4}=8\pi from each of the arguments. But checking this equality with my calculator I get something different. What am I doing wrong?
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  2. #2
    Newbie russo's Avatar
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    Re: Reducing fractions with pi in them

    Maybe something's wrong with your calculator settings. I get cos\left(\frac{35\pi}{4}\right) = cos\left(\frac{3\pi}{4}\right) = -\frac{\sqrt{2}}{2} and sin\left(\frac{35\pi}{4}\right) = sin\left(\frac{3\pi}{4}\right) = \frac{\sqrt{2}}{2}
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  3. #3
    Forum Admin topsquark's Avatar
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    Re: Reducing fractions with pi in them

    A common mistake might be at play. Make sure you are in 'radian' mode.

    -Dan
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  4. #4
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    Re: Reducing fractions with pi in them

    Ah, I should have known! Thanks!
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