Question

Biết sin α = \(\frac{7}{25}\).Tìm cos α , tan α , cot α

Answer 1

Ta có

\(\sin^2\alpha+\cos^2\alpha=1\\ \Leftrightarrow\left(\frac{7}{25}\right)^2+\cos^2\alpha=1\\ \Leftrightarrow\frac{49}{625}+\cos^2\alpha=1\\ \Leftrightarrow\cos^2\alpha=\frac{576}{625}\\ \Leftrightarrow\cos\alpha=\frac{24}{25}\)

Từ đó suy ra

\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{7}{25}:\frac{24}{25}=\frac{7}{24}\\ \cot\alpha=\frac{1}{\tan\alpha}=\frac{1}{\frac{7}{24}}=\frac{24}{7}\)