Tính sin α , tan α biết cos α = 3/4 .

16/19

Tính \(\sin \alpha ,\tan \alpha \) biết \(\cos \alpha = \frac{3}{4}\).

\(\sin \alpha = \frac{4}{{\sqrt 7 }};\tan \alpha = \frac{3}{4}\).

\(\sin \alpha = \frac{{\sqrt 7 }}{4};\tan \alpha = \frac{3}{{\sqrt 7 }}\).

\(\sin \alpha = \frac{{\sqrt 7 }}{4};\tan \alpha = \frac{{\sqrt 7 }}{3}\).

\(\sin \alpha = \frac{{\sqrt 7 }}{3};\tan \alpha = \frac{{\sqrt 7 }}{4}\).

Giải thích

Chọn C

Ta có \({\sin ^2}\alpha + {\cos ^2}\alpha = 1\) nên \({\sin ^2}\alpha = 1 - {\cos ^2}\alpha = 1 - \frac{9}{{16}} = \frac{7}{{16}}\) hay \(\sin \alpha = \frac{{\sqrt 7 }}{4}\).

Lại có \[\tan \alpha = \frac{{\sin \alpha }}{{\cos \alpha }} = \frac{{\frac{{\sqrt 7 }}{4}}}{{\frac{3}{4}}} = \frac{{\sqrt 7 }}{3}\].

Vậy \(\sin \alpha = \frac{{\sqrt 7 }}{4};\tan \alpha = \frac{{\sqrt 7 }}{3}\).