Question

Cho \(\frac{\pi}{2}< a< \frac{3\pi}{4}\). Xét dấu của các giá trị lượng giác \(cos\left(a+\frac{3\pi}{8}\right)\); \(tan\left(a-\frac{7\pi}{4}\right)\)

Answer 1

\(\frac{\pi}{2}< a< \frac{3\pi}{4}\Rightarrow\frac{7\pi}{8}< a+\frac{3\pi}{8}< \frac{9\pi}{8}\Rightarrow\frac{\pi}{2}< a+\frac{3\pi}{8}< \frac{3\pi}{2}\)

\(\Rightarrow cos\left(a+\frac{3\pi}{8}\right)< 0\)

\(\frac{\pi}{2}< a< \frac{3\pi}{4}\Rightarrow-\frac{5\pi}{4}< a-\frac{7\pi}{4}< -\pi\Rightarrow-\frac{3\pi}{2}< a< -\pi\)

\(\Rightarrow tan\left(a-\frac{7\pi}{4}\right)< 0\)