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Math Help - basic trig questions

  1. #1
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    basic trig questions

    cos13pie/12=?

    cos-pie/2=?

    sorry i cant do the symbols. thanks.
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by thatsnotalion View Post
    cos13pie/12=?

    cos-pie/2=?

    sorry i cant do the symbols. thanks.
    I'm not sure what can be assumed to be known, but here is one way to do it

    \cos\frac{13\pi}{{\color{red}12}}=\cos\left(\pi+\f  rac{\pi}{12}\right)=-\cos\frac{\pi}{12}

    Now bring the Addition Formula into play

    =-\left[\cos\left(\frac{\pi}{3}-\frac{\pi}{4}\right)\right]=-\left[\cos\frac{\pi}{3}\cdot\cos\frac{\pi}{4}+\sin\frac{  \pi}{3}\cdot\sin \frac{\pi}{4}\right]=\ldots

    As to the second problem, all you have to know is that \cos is an even function, thus

    \cos\left( -\frac{\pi}{2}\right)=\cos\left(\frac{\pi}{2}\right  )=0

    P.S: I'm a little surprised that the second problem is so much simpler, even trivial, whereas the first requires something like the Addition Formula. Is it possible that the first problem really was to determine the value of \cos\frac{13\pi}{{\color{red}2}}?
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