Question

Алгебра, 10
Найти, если...

Answer 1

$\gamma\in(\frac{3\pi }{2};2\pi) \ \Rightarrow \ Sin\gamma<0\\\\Sin\gamma=-\sqrt{1-Cos^{2}\gamma }=-\sqrt{1-(\frac{1}{\sqrt{10} })^{2} } =-\sqrt{1-\frac{1}{10} }=-\sqrt{\frac{9}{10}}=-\frac{3}{\sqrt{10} }\\\\tg\gamma=\frac{Sin\gamma}{Cos\gamma}=-\frac{3}{\sqrt{10} }:\frac{1}{\sqrt{10} }=-\frac{3\cdot \sqrt{10} }{\sqrt{10} } =\boxed{-3}$