Cho sin α = 4/5 ( 0 ∘ < α < 90 ∘ ) . Tính cos α .

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Cho \(\sin \alpha = \frac{4}{5}\)\(\left( {0^\circ < \alpha < 90^\circ } \right)\). Tính \(\cos \alpha \).

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

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

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

\(\cos \alpha = - \frac{4}{5}\).

Giải thích

Chọn B

Do \(0^\circ < \alpha < 90^\circ \Rightarrow \cos \alpha > 0\).

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