Cho \(\sin \alpha =\frac{-4}{5}\) và \(\pi <\alpha <\frac{3\pi }{2}\). Giá trị của \(\cos \alpha \) là?
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Ta có \({{\sin }^{2}}\alpha +{{\cos }^{2}}\alpha =1\Rightarrow {{\cos }^{2}}\alpha =1-{{\sin }^{2}}\alpha =1-{{\left( \frac{-4}{5} \right)}^{2}}\)
\(\Rightarrow {{\cos }^{2}}=\frac{9}{25}\Rightarrow \left[ \begin{align} & \cos \alpha =\frac{3}{5} \\ & \cos \alpha =-\frac{3}{5} \\ \end{align} \right.\).
Vì \(\pi <\alpha <\frac{3\pi }{2}\Rightarrow \cos \alpha =\frac{-3}{5}\) .
Đáp án B.
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