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Math Help - Range of values

  1. #1
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    Range of values

    Find the range of values of x bewtween 0 and \pi inclusive which satisfies

    i) sin\frac{x}{2}>0.5
    ii) cos2x<0
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  2. #2
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    Quote Originally Posted by Punch View Post
    Find the range of values of x bewtween 0 and \pi inclusive which satisfies

    i) sin\frac{x}{2}>0.5

    ii) cos2x<0
    i)

    SinA=0.5\Rightarrow\ A=30^o,\;\; A=150^o

    0.5<\ SinA\le\ 1\Rightarrow\ 30^o<A<150^o

    x=2A\Rightarrow\ 60^o<2A<300^o

    \displaystyle\ Sin\left(\frac{x}{2}\right)>0.5\Rightarrow\ 60^o<x<300^o

    For \displaystyle\ 0^o<x<180^o\Rightarrow\ Sin\left(\frac{x}{2}\right)>0.5\Rightarrow\ x>60^o

    Try the second one.
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