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Math Help - Finding trig intersection point

  1. #1
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    Finding trig intersection point

    Hi

    quick & easy question:

    6 cos 4x = 6 sin 8x
    cos 4x = sin 8x
    cos 4x = 2 sin 4x cos 4x
    1/2 = sin 4x
    arcsin(1/2) = 4x
    x = arcsin(1/2)/4

    are the above steps correct?
    If so, how can i find x in terms of pi?

    Thanks.
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  2. #2
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    e^(i*pi)'s Avatar
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    Not quite. Dividing through by \cos(4x) is potentially dividing by 0 so instead move all terms onto one side and factor

    2\sin(4x)\cos(4x) - \cos(4x) = \cos(4x)(2\sin(4x)-1) = 0

    Either \cos(4x) = 0 (these are the solutions you miss if you divide) or 2\sin(4x)-1 = 0


    As for \arcsin(0.5) recall your unit circle to see that \arcsin(0.5) = \dfrac{\pi}{6}
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