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Math Help - general solutions

  1. #1
    Senior Member
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    general solutions

    general solutions-scan10002.jpg

    I was having some confusion about the fact that the second line I wrote can be divided by 2. That would give a solution involving a power, n. Is what I have written considered better?
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  2. #2
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    Re: general solutions

    I think the problem lies mainly in your second line which is correct but confusing and hard to work with.

    Much better I think to just note that

    sin[2 theta] = -1/2 at

    (2 theta) = (11 pi)/6 + 2 pi k, and (7 pi)/6 + 2 pi k, k an integer

    Now you have two simple equations to solve w/o all the fuss about even vs. odd n etc.

    (sorry LaTex doesn't seem to be working today)

    comparing solutions

    theta = (11 pi)/12 + pi k = -pi/12 + pi k, i.e your first solution

    theta = (7 pi)/12 + pi k, i.e. your second solution

    so we ended up with the same answers but I believe my solution is a bit more straightforward than yours.

    You did get the correct answers though.
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