Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ sin\alpha =\frac{5}{13} ;tan\alpha =\frac{12}{5}\\ b.\ sin\alpha =\frac{4}{5} ;\ tan\alpha =\frac{3}{4} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ cos\ \alpha =\frac{12}{13}\\ Ta\ có:\ cos^{2} \alpha +sin^{2} \alpha =1\\ \Leftrightarrow sin\alpha =\sqrt{1-\left(\frac{12}{13}\right)^{2}} =\frac{5}{13}\\ \Leftrightarrow tan\alpha =\frac{sin\alpha }{cos\alpha } =\frac{12}{13} :\frac{5}{13} =\frac{12}{5}\\ b.\ cos\ \alpha =\frac{3}{5}\\ Ta\ có:\ cos^{2} \alpha +sin^{2} \alpha =1\\ \Leftrightarrow sin\alpha =\sqrt{1-\left(\frac{3}{5}\right)^{2}} =\frac{4}{5}\\ \Leftrightarrow tan\alpha =\frac{sin\alpha }{cos\alpha } =\frac{3}{5} :\frac{4}{5} =\frac{3}{4} \end{array}$
