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Math Help - How do I calculate this cosine?

  1. #1
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    How do I calculate this cosine?

    How do I calculate cos 7\pi/8
    I only know how to find it if it is on the unit circle >_>
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  2. #2
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    Quote Originally Posted by dorkymichelle View Post
    How do I calculate cos 7\pi/8
    I only know how to find it if it is on the unit circle >_>
    first, note that \cos\left(\frac{7\pi}{8}\right) < 0


    let x = \frac{7\pi}{4}

    use the half-angle formula ...

    \cos\left(\frac{x}{2}\right) = \pm \sqrt{\frac{1+\cos{x}}{2}}
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  3. #3
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    Why do you use [tex] x = 7\pi/4?
    and the half formula? I don't see the "half" part
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  4. #4
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    Hello dorkymichelle
    Quote Originally Posted by dorkymichelle View Post
    Why do you use [tex] x = 7\pi/4?
    and the half formula? I don't see the "half" part
    \cos x=\cos\left(\frac{7\pi}{4}\right)=\cos\left(2\pi -\frac{\pi}{4}\right) =\frac{1}{\sqrt2}

    Grandad
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  5. #5
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    Quote Originally Posted by dorkymichelle View Post
    Why do you use [tex] x = 7\pi/4?
    and the half formula? I don't see the "half" part
    \frac{1}{2} \cdot \frac{7\pi}{4} = ?
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