1. Arrange the numbers $\sin \frac{20}{19}, \cos \frac{20}{19}, \tan \frac{20}{19}, \cot \frac{20}{19}$ in ascending order. Justify your answer.
1. Since $0\cos \frac{20}{19}$ and $\operatorname{tg} \frac{20}{19}=\sin \frac{20}{19}: \cos \frac{20}{19}>\sin \frac{20}{19}$. Since $\frac{20}{19}>\frac{\pi}{3}$, then

$$
\operatorname{ctg} \frac{20}{19}<\operatorname{ctg} \frac{\pi}{3}=\frac{1}{\sqrt{3}}<\frac{\sqrt{3}}{2}=\sin \frac{\pi}{3}<\sin \frac{20}{19}
$$

Thus, the order of the numbers will be: $\cos \frac{20}{19}, \operatorname{ctg} \frac{20}{19}, \sin \frac{20}{19}, \operatorname{tg} \frac{20}{19}$.