Question

Cho Cos α =\(\dfrac{5}{12}\)Tìm Sin α ,Cot α ,Tan α

Answer 1

Ta có: \(1+tan^2a=\dfrac{1}{cos^2a}\Rightarrow tan^2a=\dfrac{1}{cos^2a}-1=\dfrac{1}{\dfrac{25}{144}}-1=\dfrac{144}{25}-1=\dfrac{119}{25}\Rightarrow tana=\dfrac{\sqrt{119}}{5}\)\(tana=\dfrac{\sqrt{119}}{5}\Rightarrow cota=\dfrac{1}{tana}=\dfrac{1}{\dfrac{\sqrt{119}}{5}}=\dfrac{5}{\sqrt{119}}\) và từ đó tính được sin a: \(tana=\dfrac{sina}{cosa}\Rightarrow sina=tana.cosa=\dfrac{\sqrt{119}}{5}.\dfrac{5}{12}=\dfrac{\sqrt{119}}{12}\)