4. Найдите tg x, если cos x = 2/√20, 3π/2 < x < 2π.

Так как \(\frac{3\pi}{2}

\[\sin x=-\sqrt{1-\cos^2x}=-\sqrt{1-\frac{4}{20}}=-\sqrt{\frac45}=-\frac{2}{\sqrt5}.\]

\[\cos x=\frac{2}{\sqrt{20}}=\frac1{\sqrt5}.\]

\[ g x=\frac{\sin x}{\cos x}=\frac{-2/\sqrt5}{1/\sqrt5}=-2.\]

Ответ: \(-2\).