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Math Help - Symmetry solutions intersecting a sinusoidal function.

  1. #1
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    Symmetry solutions intersecting a sinusoidal function.

    Set f(x) = g(x) and find the principal and
    symmetry solutions.

    f(x) = sin (2x − 1), g(x) = 1/4.

    So I have no trouble finding the principal solution...

    sin(2x-1)=1/4
    2x-1=.2526
    2x=1.2526
    x=.6263

    Now how on earth do I about solving for the symmetry solution without cheating using a graph? I know, or at least think, you have to relate it to a minimum or maximum, but this becomes difficult without a graph because I'm not entirely sure where the solution I have is located. How do you solve this with just plain equations? I'm reviewing precalc/calc after a 5 year hiatus and only have myself and an old text book and the text book isn't much for help.

    Thanks!
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  2. #2
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    Re: Symmetry solutions intersecting a sinusoidal function.

    Sines are positive in the first and second quadrants.
    So 2x-1= .2526 or pi-.2426 or 2pi+.2526 or 3pi-.2426 etc
    So a formula for these answers is npi+(-1)^n(.2526)
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  3. #3
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    Re: Symmetry solutions intersecting a sinusoidal function.

    Thanks! I think what I was missing was I trying x= pi-.2526, ignoring the 2x-1 for some reason. But I've got the idea now.
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