Cho \(\tan\alpha=-\dfrac{3}{4}\) và \(\dfrac{\pi}{2}< \alpha< \pi\). Tính \(\sin a\).
\(\dfrac{3}{5}\).\(-\dfrac{3}{5}\).\(\dfrac{4}{5}\).\(-\dfrac{4}{5}\).Hướng dẫn giải:Có \(\dfrac{1}{\cos^2\alpha}=1+\tan^2\alpha\) \(\Rightarrow\cos^2\alpha=\dfrac{16}{25}\)
Có \(\sin^2\alpha+\cos^2\alpha=1\Rightarrow\sin^2\alpha=\dfrac{9}{16}\) mà \(\dfrac{\pi}{2}< \alpha< \pi\) \(\Rightarrow\sin\alpha>0\Rightarrow\sin\alpha=\dfrac{3}{5}\)
