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Math Help - Inequality.

  1. #1
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    Inequality.

    I've got something like this:

    I need to find s that makes the following inequality true.

    \displaystyle\left|\frac{6s\cos x +1 - 6s}{-2s(\cos x -1) + 1}\right|\le 1

    Using some trig identities I got it down to -4s\sin^2(x/2)-2\le -12s\sin^2(x/2)\le 4s\sin^2(x/2)

    which I think is correct, but I don't know what to do now...
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  2. #2
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    If you put in s = 0 you will get equality. That works just fine if you are looking for one solution. However, there are more solutions and from what I was able to graph they all lie in the interval  s \in [0,t] for some real, positive number t.
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  3. #3
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    Thanks, I worked it out by breaking the inequality into two separate ones and eventually found the answer to be s <= 1/4
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