Question

Tính \(\cos\alpha;tan\alpha;\cot\alpha\)

biết \(\sin\alpha=\frac{5}{13}\)

Answer 1

\(\sin\alpha=\frac{5}{13}\) => \(\sin^2\alpha=\frac{25}{169}\)

Mà \(\cos^2\alpha+\sin^2\alpha=1\) nên \(\cos^2\alpha=\frac{144}{169}\) => \(\cos\alpha=\frac{12}{13}\)

Ta có \(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}\) => \(\tan\alpha=\frac{5}{13}:\frac{12}{13}=\frac{5}{12}\)

Lại có \(\cot\alpha=\frac{\cos\alpha}{\sin\alpha}\) =>  \(\cot\alpha=\frac{12}{13}:\frac{5}{13}=\frac{12}{5}\)

Chúc bạn làm bài tốt

Answer 2

Ta có \(\sin^2\alpha+\cos^2\alpha=1\)

\(\Rightarrow\cos^2\alpha=1-\sin^2\alpha\)

\(\Rightarrow\cos^2\alpha=1-\frac{25}{169}=\frac{144}{169}\Rightarrow\cos\alpha=\frac{12}{13}\)

Ta lại có \(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{5}{13}.\frac{13}{12}=\frac{5}{12}\Rightarrow\cot\alpha=\frac{12}{5}\)