# Math Help - Range of values

1. ## 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) $cos2x<0$

2. Originally Posted by Punch
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

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

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

For $\displaystyle\ 0^o0.5\Rightarrow\ x>60^o$

Try the second one.