Cho sin α = 4/5 , pi/ 2 < α < pi . Tính cos α .

7/39

Cho \(\sin \alpha = \frac{4}{5},\,\,\frac{\pi }{2} < \alpha < \pi \). Tính \(\cos \alpha \).

\(\cos \alpha = - \frac{3}{5}\).

\(\cos \alpha = - \frac{1}{5}\).

\(\cos \alpha = \frac{3}{5}\).

\(\cos \alpha = \frac{1}{5}\).

Giải thích

Chọn A

\({\sin ^2}\alpha + {\cos ^2}\alpha = 1 \Rightarrow {\cos ^2}\alpha = 1 - {\sin ^2}\alpha = 1 - {\left( {\frac{4}{5}} \right)^2} = \frac{9}{{25}} \Rightarrow \cos \alpha = \pm \frac{3}{5}\)

Vì \(\frac{\pi }{2} < \alpha < \pi \) nên \(\cos \alpha = - \frac{3}{5}\).