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Math Help - Trigonometric functions

  1. #1
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    Trigonometric functions

    The function y=sin(x-p)+d has a vertical translation of -3 and passes through the point (pi/6, -2). Determine the values of p and d

    My attempt
    d= -3
    -2= sin (pi/6 - p) -3
    1 = 1/2 - sinp
    1-1/2= - sinp
    1/2= - sinp
    -1/2= sinp

    The question didn't specify a domain so how would I find the value of p?
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  2. #2
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    Re: Trigonometric functions

    Quote Originally Posted by xoxo View Post
    The function y=sin(x-p)+d has a vertical translation of -3 and passes through the point (pi/6, -2). Determine the values of p and d

    My attempt
    d= -3
    -2= sin (pi/6 - p) -3
    1 = 1/2 - sinp
    note ...

    {\color{red}\sin\left(\frac{\pi}{6} - p\right) \ne \sin\left(\frac{\pi}{6}\right) - \sin{p}}
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  3. #3
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    Re: Trigonometric functions

    -2 = sin ( π/6-p)-3
    Or
    sin ( π/6-p)=1=sin⁡ π/2
    Therefore one of the solution would be
    π/6-p = π/2 That gives p = - π/3
    Last edited by ibdutt; January 1st 2013 at 12:53 AM.
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