Question

     Stiind ca x ∈ $(\frac{ \pi }{2};\pi)$ si ca sinx = $\frac{3}{5}$, sa se calculeze sin ${ \frac{x}{2} }$.

Answer 1

$sin\frac{x}{2}= \sqrt{ \frac{1-cosx}{2} }$
cosx=-$-\sqrt{1- sin^{2}x }= -\sqrt{1- \frac{9}{25} }=- \frac{4}{5}$
$sin \frac{x}{2}= \sqrt{ \frac{1+ \frac{4}{5} }{2} }$
$sin \frac{x}{2}= \frac{3}{ \sqrt{10} }$