Question

найдите sina если cosa= -2/10,а принадлежит(пи; 3пи/2)

Answer 1

$\alpha\in(\pi \ ; \ \frac{3\pi }{2}) \ \Rightarrow \ Sin\alpha<0\\\\Sin\alpha=-\sqrt{1-Cos^{2}\alpha}=-\sqrt{1-\Big(-\dfrac{2}{10}\Big)^{2}} =-\sqrt{1-\dfrac{4}{100} }=\\\\=-\sqrt{\dfrac{96}{100} }=-\sqrt{\dfrac{24}{25} }=-\dfrac{2\sqrt{6} }{5}\\\\\boxed{Sin\alpha=-\dfrac{2\sqrt{6} }{5}}$