Question

[Trần Kim Bao]

Cho góc nhọn α. Tính tỉ số lượng giác còn lại nếu cotα= 40/9

Answer 1

[Gia Huy]

\(cot\alpha=\dfrac{40}{9}\Rightarrow tan\alpha=\dfrac{1}{cot\alpha}=\dfrac{1}{\dfrac{40}{9}}=\dfrac{9}{40}\)

+) \(\dfrac{1}{cos^2\alpha}=1+tan^2\alpha\)

\(\Leftrightarrow\dfrac{1}{cos^2\alpha}=1+\left(\dfrac{9}{40}\right)^2\\ \Rightarrow cos\alpha=\sqrt{1:\left(1+\left(\dfrac{9}{40}\right)^2\right)}=\dfrac{40}{41}\)

+) \(sin^2\alpha=1-cos^2\alpha\)

\(\Leftrightarrow sin\alpha=\sqrt{1-cos^2\alpha}=\sqrt{1-\left(\dfrac{40}{41}\right)^2}=\dfrac{9}{41}\)