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Math Help - transformation of sine graph

  1. #1
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    transformation of sine graph

    Hi , I need help with the following . The first part is write down the equation of y= f(x) given the sketch attached .
    The second part is to sketch the graph of 1+2 f(x - 90)
    I don't know if the 180 on the sketch given is correct but i take the sketch given as y=2sin2x
    and 1+2 f(x - 90) evaluates to 1-2sin2x . Is this right ?

    Thank you
    Attached Thumbnails Attached Thumbnails transformation of sine graph-test.jpg  
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  2. #2
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    Re: transformation of sine graph

    When x=180^\circ, we have 2\sin(2x)=2\sin(360)=0, not -2.
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  3. #3
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    Re: transformation of sine graph

    I understand that that at 180 y=2sin2x=0 but has the 180 on the sketch been placed too far to the left .
    From observation y=2sin2x would give the minimum as (135,-2) .
    What is the equation if you take (180,-2) as the minimum ?
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  4. #4
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    Re: transformation of sine graph

    Quote Originally Posted by minicooper58 View Post
    I understand that that at 180 y=2sin2x=0 but has the 180 on the sketch been placed too far to the left .
    From observation y=2sin2x would give the minimum as (135,-2) .
    Yes, the image is not clear. However, the minimum point seems to the right of the fifth tick on the x-axis. Therefore, if 180 corresponds to the that tick, then the minimum point has to be > 180 and not 135. The digits "180" themselves seem to be located directly above the minimum.

    Quote Originally Posted by minicooper58 View Post
    What is the equation if you take (180,-2) as the minimum ?
    The first positive minimum point of \sin(kx) is 180 iff k\cdot180=270.
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  5. #5
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    Re: transformation of sine graph

    What would you say the equation of y=f(x) is ?
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  6. #6
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    Re: transformation of sine graph

    It's y=2\sin(kx) for some k. The equation to find k is given in post #4. I hope that you understand how this equation arises or that you will ask further questions about it.
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  7. #7
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    Re: transformation of sine graph

    Hi , I understand y=2sinkx is the only possible equation given the sketch but if 180 say should have been the endpoint of the sketch ,
    then is the equation y=2sin2x with the minimum at (135,-2)
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  8. #8
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    Re: transformation of sine graph

    Quote Originally Posted by minicooper58 View Post
    if 180 say should have been the endpoint of the sketch, then is the equation y=2sin2x with the minimum at (135,-2)
    If by the "endpoint of the sketch" you mean "the second positive zero of f(x)," then yes, f(x) = 2sin(2x) has the endpoint at x = 180 and (135, -2) is the minimum.
    Thanks from minicooper58
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  9. #9
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    Re: transformation of sine graph

    notice on the sketch that the positive zero of f(x) is not reached but the sketch starts before 0 , indication possibly that the 180 has been marked in error .
    Many thanks for your help . Apologies for the poor sketch .
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