Question

Stiind x∈(π,3π/2) si cosx = 2√6/5. Calculati sinx

Answer 1

[tex]x este in cadranu III unde sin x \ \textless \ 0., deci.sin x= - \sqrt{1- cos^{2}x [/tex]

Deci sin x = -$\sqrt{1- cos^{2} x} = - \sqrt{1- ( \frac{ 2\sqrt{6} }{6} ) ^{2}$ 
Obtinem: sin x= -$\sqrt{1- \frac{24}{25} }= -\sqrt{ \frac{1}{25} } = - \frac{1}{5}.$