Cho góc \(\alpha\) thỏa mãn \(\sin\alpha=\dfrac{12}{13}\) và \(\dfrac{\pi}{2}<\alpha<\pi\). Tính \(\cos\alpha\).
![]() | \(\cos\alpha=\dfrac{1}{13}\) |
![]() | \(\cos\alpha=\dfrac{5}{13}\) |
![]() | \(\cos\alpha=-\dfrac{5}{13}\) |
![]() | \(\cos\alpha=-\dfrac{1}{13}\) |
Chọn phương án C.
Vì \(\dfrac{\pi}{2}<\alpha<\pi\) nên \(\cos\alpha<0\).
Ta có \(\cos^2\alpha=1-\sin^2\alpha=1-\dfrac{144}{169}=\dfrac{25}{169}\).
Suy ra \(\cos\alpha=-\dfrac{5}{13}\).