1)Prove that $\displaystyle \sin 1^{\circ}$ and $\displaystyle \cos 1^{\circ}$ are irrational.

3)Suppose that $\displaystyle \sum_{k=0}^n k^m = P_m(n)$ where $\displaystyle P_m$ is an $\displaystyle m+1$-degree polynomial. Prove that the leading coefficient of $\displaystyle P_m$ is $\displaystyle 1/(m+1)$.