Question

cos a= -2/3 , 180градусов

Answer 1

$\displaystyle\bf\\180^\circ < \alpha < 270^\circ \ \ \ \Rightarrow \ \ \ Sin\alpha < 0\\\\\\Cos\alpha =-\frac{2}{3} \\\\\\Sin\alpha =-\sqrt{1-Cos^{2}\alpha } =-\sqrt{1-\Big(-\frac{2}{3} \Big)^{2} } =-\sqrt{1-\frac{4}{9} }=\\\\\\=-\sqrt{\frac{5}{9} }=-\frac{\sqrt{5} }{3} \\\\\\Sin2\alpha =2Sin\alpha Cos\alpha =2\cdot\Big(-\frac{\sqrt{5} }{3} \Big)\cdot\Big(-\frac{2}{3} \Big)=\frac{4\sqrt{5} }{9}$