Question

[Piii]

α+β=90^o ,tanβ=5/3

tinh ti so luong giac α

Answer 1

[Nguyễn Việt Lâm]

\(a+b=90\Rightarrow a=90-b\Rightarrow tana=tan\left(90-b\right)=cotb=\dfrac{1}{tanb}=\dfrac{3}{5}\)

\(\dfrac{sina}{cosa}=tana=\dfrac{3}{5}\Rightarrow sina=\dfrac{3cosa}{5}\)

Mà \(sin^2a+cos^2a=1\Rightarrow\dfrac{9}{25}cos^2a+cos^2a=1\Rightarrow\dfrac{34}{25}cos^2a=1\)

\(\Rightarrow cos^2a=\dfrac{25}{34}\Rightarrow cosa=\dfrac{5}{\sqrt{34}}\) (do a<90 nên cosa>0)

\(\Rightarrow sina=\dfrac{3}{5}cosa=\dfrac{3}{5}\dfrac{5}{\sqrt{34}}=\dfrac{3}{\sqrt{34}}\)

Vậy \(sina=\dfrac{3}{\sqrt{34}};cosa=\dfrac{5}{\sqrt{34}};tana=\dfrac{3}{5};cota=\dfrac{5}{3}\)