Question

1) Cho \(\sin\alpha=\dfrac{1}{2}\). Tính \(\cos\alpha,\tan\alpha,\cot\alpha\).

2) Cho \(\cos\alpha=\dfrac{\sqrt{2}}{2}\). Tính \(\sin\alpha,\tan\alpha,\cot\alpha\).

Answer 1

1) Ta có: \(\sin\alpha=\dfrac{1}{2}\Rightarrow\alpha=30^\circ\)

\(\Rightarrow\cos\alpha=\dfrac{\sqrt{3}}{2}\)

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

\(\Rightarrow\cot\alpha=\dfrac{1}{\tan\alpha}=\dfrac{3}{\sqrt{3}}\)

2) Ta có: \(\cos\alpha=\dfrac{\sqrt{2}}{2}\Rightarrow\alpha=45^{\circ}\)

\(\Rightarrow\sin\alpha=\dfrac{\sqrt{2}}{2}\)

\(\Rightarrow\tan\alpha=\dfrac{\sin\alpha}{\cos\alpha}=\dfrac{\dfrac{\sqrt{2}}{2}}{\dfrac{\sqrt{2}}{2}}=1\)

\(\Rightarrow\cot\alpha=\dfrac{1}{\tan\alpha}=1\)