Question

Cho \(\tan\alpha=-3\) và \(\dfrac{\pi}{2}< \alpha< \pi.\)Tính \(\cos\alpha\),\(\sin\alpha\),\(\cot\alpha\)

Answer 1

Lời giải:

$\frac{\pi}{2}< a< \pi$ nên $\sin a>0; \cos a< 0$

$-3=\tan a=\frac{\sin a}{\cos a}\Rightarrow \sin a=-3\cos a$

$\Rightarrow \sin ^2a=9\cos ^2a$

$\Rightarrow 10\sin ^2a=9(\sin ^2a+\cos ^2a)=9$

$\Rightarrow \sin ^2a=\frac{9}{10}$

$\Rightarrow \sin a=\frac{3}{\sqrt{10}}$

$\cos a=\frac{\sin a}{-3}=\frac{-1}{\sqrt{10}}$

$\cot a=\frac{1}{\tan a}=\frac{-1}{3}$