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Math Help - Sin(2x)=cos(x)

  1. #1
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    Sin(2x)=cos(x)

    Find the point of intersection of f(x):cos(x) and g(x):sin(2x) in the intervall 0;Pi/2
    is there no way to find the point but by approximation?
    Thanks
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Schdero View Post
    Find the point of intersection of f(x):cos(x) and g(x):sin(2x) in the intervall 0;Pi/2
    is there no way to find the point but by approximation?
    Thanks
    You can find the exact solutions! Recall that \sin(2x)=2\sin x\cos x.

    So 2\sin x\cos x=\cos x\implies (2\sin x-1)\cos x=0.

    So either \sin x=\tfrac{1}{2} or \cos x=0. Now you can find exact solutions, keeping in mind they must fall in the interval [0,\pi/2].

    Can you take it from here?
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  3. #3
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Schdero View Post
    Find the point of intersection of f(x):cos(x) and g(x):sin(2x) in the intervall 0;Pi/2
    is there no way to find the point but by approximation?
    Thanks
    \sin(2x)=2\sin(x)\cos(x).......
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  4. #4
    Junior Member slovakiamaths's Avatar
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    Dear, the only poit of intersaction is \frac{\pi}{4}
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  5. #5
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by slovakiamaths View Post
    Dear, the only poit of intersaction is \frac{\pi}{4}
    That would be true if the user was to find the intersection between cos(x) and sin(x)....

    In this case, there are two solutions...
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  6. #6
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    I see, thanks! But I see also that i seem to lack most of these rules, does amyone have a link where they are listed or could anyone tell me the most important rules?
    Thanks for the help
    Last edited by Schdero; April 29th 2010 at 12:22 PM.
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  7. #7
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    List of trigonometric identities - Wikipedia, the free encyclopedia contains probably anything you will ever need.
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  8. #8
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    This is way to complicated, I dont even see which formula are relevant for my level of mathematics. I'd need a site on which the basic rules are listed, which i need for basic calculus exercises. Unfortunately i either found way to complex or way to simple sites...
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  9. #9
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    Quote Originally Posted by Schdero View Post
    This is way to complicated, I dont even see which formula are relevant for my level of mathematics. I'd need a site on which the basic rules are listed, which i need for basic calculus exercises. Unfortunately i either found way to complex or way to simple sites...
    1. It's your responsibility to use an appropriate serach engine (such as Google) to find and review sites in order to find a site that suits your purpose.

    2. \sin(2x) = \cos(x) \Rightarrow \sin(2x) = \sin\left( \frac{\pi}{2} - x\right).

    Case 1: 2x = \frac{\pi}{2} - x.

    Case 2: 2x = \pi - \left( \frac{\pi}{2} - x\right).

    In each case, solve for x.
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