Question

 Tìm sin ∝ ; cos ∝ biết :

1. \(\tan a=\dfrac{1}{3}\)

2.\(\cot a=\dfrac{3}{4}\)

Answer 1

1. Ta có \(1+\tan\alpha=\dfrac{1}{\cos^2\alpha}\Rightarrow\dfrac{1}{\cos^2\alpha}=1+\dfrac{1}{3}\Rightarrow\dfrac{1}{\cos^2\alpha}=\dfrac{4}{3}\Rightarrow\cos^2\alpha=\dfrac{3}{4}\Rightarrow\cos\alpha=\dfrac{\sqrt{3}}{2}\)

Mặt khác, \(tan\alpha=\dfrac{1}{3}=\dfrac{\sin\alpha}{\cos\alpha}\Rightarrow\sin\alpha=\dfrac{\cos a}{3}=\dfrac{\dfrac{\sqrt{3}}{2}}{3}=\dfrac{1}{2\sqrt{3}}\)

2. Ta có \(1+\cot^2\alpha=\dfrac{1}{\sin^2\alpha}\Rightarrow\dfrac{1}{\sin^2\alpha}=1+\dfrac{9}{16}\Rightarrow\dfrac{1}{\sin^2\alpha}=\dfrac{25}{16}\Rightarrow\dfrac{1}{\sin a}=\dfrac{5}{4}\Rightarrow\sin\alpha=\dfrac{4}{5}\)

Mặt khác, \(\cot\alpha=\dfrac{\cos\alpha}{\sin\alpha}\Rightarrow\cos\alpha=\sin\alpha.\cot\alpha=\dfrac{3}{4}.\dfrac{4}{5}=\dfrac{3}{5}\)