Cho \(\cos \alpha=\frac{2}{3} ;\left(0^{\circ} var DOMAIN =...

* Hướng dẫn giải

Ta có

\(\sin ^{2} \alpha+\cos ^{2} \alpha=1\)

\(\Rightarrow \sin \alpha=\sqrt{1-\cos ^{2} \alpha}\)

\(\begin{aligned} \Rightarrow\sin \alpha &=\sqrt{1-\left(\frac{2}{3}\right)^{2}} \\ &=\sqrt{1-\frac{4}{9}} \\ &=\sqrt{\frac{5}{9}} \\ &=\frac{\pm\sqrt{5}}{3} \end{aligned}\)

mà \(0^{\circ}<\alpha<90^{\circ}\Rightarrow sin\alpha =\frac{\sqrt{5}}{3}\)