Question

Найдите tg(α), если sin= $frac{3}{sqrt{10} }$

Answer 1

$sina=frac{3}{sqrt{10}}>0; ; Rightarrow ; ; ain (2pi n,;pi +2pi n)\\boxed{sin^2a+cos^2a=1}; ; to ; ; cos^2a=1-sin^2a=1-frac{9}{10}=frac{1}{10}; ,; ; cosa=pm frac{1}{sqrt{10}}\\boxed {tga=frac{sina}{cosa}}; ; ,; ; tga=frac{frac{3}{sqrt{10}}}{pm frac{1}{sqrt{10}}}=pm frac{3}{1}=pm 3\\\Esli; ; ain (2pi n, ;frac{pi }{2}+2pi n); ,; to; ; tga=3; .\\Esli; ain (frac{pi}{2}+2pi n, ;pi +2pi n); ; ,; to ; ; tga=-3; .$