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Math Help - Solve for x

  1. #1
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    Solve for x

    Solve for x: sin x = cos (2x + 15)
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  2. #2
    Eater of Worlds
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    sin(x)=cos(2x+15)

    cos^{-1}(sin(x))=2x+15

    \frac{\pi}{2}-sin^{-1}(sin(x))=2x+15

    Continue?.

    How many solutions are you looking for?. In a certain interval?. Just one?.
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  3. #3
    Flow Master
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    Quote Originally Posted by galactus View Post
    sin(x)=cos(2x+15)

    cos^{-1}(sin(x))=2x+15

    \frac{\pi}{2}-sin^{-1}(sin(x))=2x+15

    Continue?.

    How many solutions are you looking for?. In a certain interval?. Just one?.
    I'll just add a bit of background:

    \sin x = \cos \left(\frac{\pi}{2} - x \right) and so the equation can be written as \cos \left(\frac{\pi}{2} - x \right) = \cos (2x + 15).

    Now you need to understand the symmetry of the unit circle: \cos A = \cos B means that either A = B + 2 n \pi or A = -B + 2 n \pi where n is an integer.
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  4. #4
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    Thanks....

    I want to thank both replies. I am learning a lot here.
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