Question

Cho \(\pi< \alpha< \dfrac{3\pi}{2}\). Xác định dấu của các giá trị lượng giác sau :

a) \(\cos\left(\alpha-\dfrac{\pi}{2}\right)\)

b) \(\sin\left(\dfrac{\pi}{2}+\alpha\right)\)

c) \(\tan\left(\dfrac{3\pi}{2}-\alpha\right)\)

d) \(\cot\left(\alpha+\pi\right)\)

Answer 1

Do \(\pi< \alpha< \dfrac{3\pi}{2}\) nên \(sin\alpha,cos\alpha< 0;tan\alpha,cot\alpha< 0\).
\(cos\left(\alpha-\dfrac{\pi}{2}\right)=cos\left(\dfrac{\pi}{2}-\alpha\right)=sin\alpha< 0\).
\(sin\left(\dfrac{\pi}{2}+\alpha\right)=cos\alpha< 0\).
\(tan\left(\dfrac{3\pi}{2}-\alpha\right)=tan\left(\dfrac{3\pi}{2}-\alpha-2\pi\right)\)\(=tan\left(-\dfrac{\pi}{2}-\alpha\right)\)\(=-tan\left(\dfrac{\pi}{2}+\alpha\right)=cot\left(\alpha\right)>0\).
\(cot\left(\alpha+\pi\right)=cot\left(\alpha\right)>0\).