Cho sin alpha = 4/5 ( 90 độ < alpha < 180 độ) Tính cos alpha

10/21

Cho \[\sin \alpha = \frac{4}{5}\,\,\left( {{{90}^0} < \alpha < {{180}^0}} \right)\]. Tính \[{\rm{cos}}\alpha \]

\[c{\rm{os}}\alpha = \frac{3}{5}\].

\[c{\rm{os}}\alpha = \frac{5}{3}\]

\[c{\rm{os}}\alpha = - \frac{3}{5}\].

\[{\rm{cos}}\alpha = - \frac{4}{5}\]

Giải thích

Chọn C

Ta có: \[{\sin ^2}\alpha + c{\rm{o}}{{\rm{s}}^2}\alpha = 1 \Leftrightarrow c{\rm{o}}{{\rm{s}}^2}\alpha = 1 - {\sin ^2}\alpha \Leftrightarrow c{\rm{os}}\alpha = \pm \sqrt {1 - {{\sin }^2}\alpha } = \pm \sqrt {1 - {{\left( {\frac{4}{5}} \right)}^2}} = \pm \frac{3}{5}\]

Vì \[{90^0} < \alpha < {180^0}\]nên \[c{\rm{os}}\alpha = - \frac{3}{5}\]