Question

Biết

\(sin\) \(\alpha\)=\(\frac{5}{13}\). Tính \(cos\)\(\alpha\), \(tan\)\(\alpha\), \(cot\)\(\alpha\)

Answer 1

\(sin^2a+cos^2a=1\)

\(\Rightarrow cos^2a=1-\left(\frac{5}{13}\right)^2\)

\(\Rightarrow cos^2a=\frac{144}{169}\)

\(\Rightarrow cosa=\sqrt{\frac{144}{169}}=\frac{12}{16}\)

Ta có : \(cotga=\frac{cosa}{sina}=\frac{5}{13}:\frac{12}{16}=\frac{12}{5}\)

\(tana.cotga=1\)

\(\Rightarrow tan\alpha=1:\frac{12}{5}\)

\(\Rightarrow tan\alpha=\frac{5}{12}\)

Answer 2

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