Question

Bài 1: Cho góc nhọn α, biết sin α =\(\frac{3}{5}.\) Hãy tính: cos α, tan α, cotag α

Bài 2: Cho góc nhọn α, biết cos α =0,8. Tính sin α, cotag α, tan α

giải hộ mk nhé mn

Answer 1

1.\(\sin^2\alpha+\cos^2\alpha=1\)

\(\Rightarrow\cos^2\alpha=1-\sin^2\alpha=1-\left(\frac{3}{5}\right)^2=1-\frac{9}{25}=\frac{16}{25}\)

\(\Rightarrow\cos\alpha=\frac{4}{5}\)

\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{\frac{3}{5}}{\frac{4}{5}}=\frac{3}{4}\)

\(\cot\alpha=\frac{\cos\alpha}{\sin\alpha}=\frac{\frac{4}{5}}{\frac{3}{5}}=\frac{4}{3}\)

2.\(\sin^2\alpha+\cos^2\alpha=1\)

\(\Rightarrow\sin^2\alpha=1-\cos^2\alpha=1-\left(0,8\right)^2=1-0,64=0,36\)

\(\Rightarrow\sin\alpha=0,6\)

\(\tan\alpha=\frac{\sin\alpha}{\cos\alpha}=\frac{0,6}{0,8}=\frac{3}{4}\)

\(\tan\alpha.\cot\alpha=1\Rightarrow\cot\alpha=\frac{1}{\tan\alpha}=\frac{1}{\frac{3}{4}}=\frac{4}{3}\)