Cho góc alpha biết sin alpha = -2/5 và 3 pi /2 < alpha < 2pi . Tính cos alpha :

Chọn C

Ta có: \[{\sin ^2}\alpha  + {\cos ^2}\alpha  = 1\]\[ \Rightarrow {\cos ^2}\alpha \,{\rm{ = }}\,{\rm{1}} - {\rm{si}}{{\rm{n}}^2}\alpha  = 1 - \frac{4}{{25}} = \frac{{21}}{{25}}\]\( \Leftrightarrow \left[ \begin{array}{l}\cos \alpha  = \frac{{\sqrt {21} }}{5}\\\cos \alpha  =  - \frac{{\sqrt {21} }}{5}\end{array} \right.\).

Vì \(\frac{{3\pi }}{2} < \alpha  < 2\pi \)nên \(\cos \alpha  > 0\)\( \Rightarrow {\rm{cos}}\alpha  = \frac{{\sqrt {21} }}{5}\).