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Math Help - Trigonometric functions, arcus functions

  1. #1
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    Cool Trigonometric functions, arcus functions

    Determine arccos(sin 49*pi /8)
    The answer can be written in the form a/b where a/b is an abbreviated fraction.

    a =?
    b =?
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  2. #2
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    Quote Originally Posted by sf1903 View Post
    Determine arccos(sin 49*pi /8)
    The answer can be written in the form a/b where a/b is an abbreviated fraction.

    a =?
    b =?

    \sin A = \cos (\frac{\pi}{2} - A) and

    \sin (2\pi+A) =\sin A

    \cos ^{-1} (\cos A) = A

    ok

    \cos ^{-1} (\sin \frac{49\pi}{8}) but

    \frac{49\pi}{8} = 6\pi + \frac{\pi}{8} = 3(2\pi) + \frac{\pi}{8}

    so

    \cos ^{-1} ( \sin \frac{\pi}{8})

    \cos ^{-1} (\cos (\frac{\pi}{2} - \frac{\pi}{8}))=\frac{\pi}{2} - \frac{\pi}{8}
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