Question

Bài 3: Cho ∆ABC vuông tại A. AB/BC = 1/2.Tính Sin alpha, Cos alpha, Tân alpha

Answer 1

Ta có: \(\dfrac{AB}{BC}=\dfrac{1}{2}\)

\(\Rightarrow cos\alpha=\dfrac{1}{2}\)

Mà: \(sin^2\alpha+cos^2\alpha=1\)

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

\(\Rightarrow sin^2\alpha=1-\dfrac{1}{2}\)

\(\Rightarrow sin^2\alpha=\dfrac{1}{2}\)

\(\Rightarrow sin\alpha=\sqrt{\dfrac{1}{2}}=\dfrac{\sqrt{2}}{2}\)

Mà: \(tan\alpha=\dfrac{sin\alpha}{cos\alpha}\)

\(\Rightarrow tan\alpha=\dfrac{\dfrac{\sqrt{2}}{2}}{\dfrac{1}{2}}\)

\(\Rightarrow tan\alpha=\sqrt{2}\)