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Math Help - solve the equations

  1. #1
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    solve the equations

    Could anyone help me these problems, thanks very much.

    Solve the equations:

    i) cos2x = sinx

    ii) sin2x - 1 = cos2x

    Giving the answers in radians in the range 0 to 2\pi

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  2. #2
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    Quote Originally Posted by srobrien View Post
    Could anyone help me these problems, thanks very much.

    Solve the equations:

    i) cos2x = sinx

    ii) sin2x - 1 = cos2x

    Giving the answers in radians in the range 0 to 2\pi

    HI

    (1) \cos 2x=\sin x

    1-2\sin^2 x =\sin x

    2\sin^2 x+\sin x-1=0

    (2\sin x-1)(\sin x+1)=0

    So 2\sin x-1=0 OR \sin x+1=0

    Continue from here ..

    (2) \sin 2x-1=\cos 2x

    2\sin x\cos x -\cos^2 x -\sin^2 x =\cos^2 x-\sin^2 x

    2\cos^2 x-2\sin x\cos x=0

    \cos^2 x-\sin x\cos x=0

    \cos x(\cos x-\sin x)=0

    \cos x=0 OR \cos x-\sin x=0\Rightarrow \tan x=1

    Continue from here .
    Last edited by mathaddict; October 28th 2009 at 01:26 AM.
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  3. #3
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    Thank you
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  4. #4
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    Quote Originally Posted by mathaddict View Post
    HI

    (1) \cos 2x=\sin x

    2\sin x\cos x =\sin x
    Are you sure?
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  5. #5
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    Quote Originally Posted by james_bond View Post
    Are you sure?
    Edited . THanks for pointing out , ok now ?
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  6. #6
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    Yeah (I hope). Thanks for correcting.
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