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

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

    Hi

    Again I have to find the point of intersection of these two functions.
    I know cos(2x) = cos(x)^2-sin(x)^2

    But still: sin(x)=cos(x)^2-sin(x)^2, i have no idea how to solve that. I reached the point (1+sin(x))=tan(x)cos(x), but i don't get further. Anybody who can help to find the exact solution?
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  2. #2
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    Quote Originally Posted by Schdero View Post
    Hi

    Again I have to find the point of intersection of these two functions.
    I know cos(2x) = cos(x)^2-sin(x)^2

    But still: sin(x)=cos(x)^2-sin(x)^2, i have no idea how to solve that. I reached the point (1+sin(x))=tan(x)cos(x), but i don't get further. Anybody who can help to find the exact solution?
    hi

    hint : cos 2x = 1-2sin^2 x
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  3. #3
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    Quote Originally Posted by Schdero View Post
    Hi

    Again I have to find the point of intersection of these two functions.
    I know cos(2x) = cos(x)^2-sin(x)^2

    But still: sin(x)=cos(x)^2-sin(x)^2, i have no idea how to solve that. I reached the point (1+sin(x))=tan(x)cos(x), but i don't get further. Anybody who can help to find the exact solution?
    \cos^2(x) = 1-\sin^2(x)

    Consequently

    \cos(2x) = 1-2\sin^2(x)
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  4. #4
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    Quote Originally Posted by Schdero View Post
    Hi

    Again I have to find the point of intersection of these two functions.
    I know cos(2x) = cos(x)^2-sin(x)^2

    But still: sin(x)=cos(x)^2-sin(x)^2, i have no idea how to solve that. I reached the point (1+sin(x))=tan(x)cos(x), but i don't get further. Anybody who can help to find the exact solution?
    Hi,

    How about this?

    sin(x) = cos(x)^2-sin(x)^2
    sin(x) = 1 - sin(x)^2 - sin(x)^2
    2sin(x)^2 + sin(x) - 1 = 0
    (2sin(x) - 1)(sin(x) + 1) = 0
    sin(x) = -1/2 or sin(x) = 1

    then solve for x.. =)
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  5. #5
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    perfect, thanks!
    I somehow simply don't connect the sin/cos rules well...
    thanks again!
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  6. #6
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    Quote Originally Posted by Schdero View Post
    Hi

    Again I have to find the point of intersection of these two functions.
    I know cos(2x) = cos(x)^2-sin(x)^2

    But still: sin(x)=cos(x)^2-sin(x)^2, i have no idea how to solve that. I reached the point (1+sin(x))=tan(x)cos(x), but i don't get further. Anybody who can help to find the exact solution?
    Another approach is suggested by noting that sin(A) = cos(B) => sin(A) = sin(pi/2 - B).

    Therefore A = pi/2 - B or A = pi - (pi/2 - B) ....
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