1. ## Range of values

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

i) $\displaystyle sin\frac{x}{2}>0.5$
ii) $\displaystyle cos2x<0$

2. Originally Posted by Punch
Find the range of values of $\displaystyle x$ bewtween $\displaystyle 0$ and $\displaystyle \pi$ inclusive which satisfies

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

ii) $\displaystyle cos2x<0$
i)

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

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

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

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

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

Try the second one.