G8.3 There are exactly $N$ values of $\alpha$ satisfying the equation $\cos ^{3} \alpha-\cos \alpha=0$, where $0^{\circ} \leq \alpha \leq 360^{\circ}$. Find $N$.

G8.4 If the $N^{\text {th }}$ day of May in a year is Thursday and the $K^{\text {th }}$ day of May in the same year is Monday, where $10<K<20$, find $K$.
$\begin{array}{l}\cos \alpha(\cos \alpha+1)(\cos \alpha-1)=0 \\ \cos \alpha=0,-1 \text { or } 1 \\ \alpha=90,270,180,0,360 \\ \Rightarrow N=5 \\ 5^{\text {th }} \text { May is Thursday } \\ 9^{\text {th }} \text { May is Monday } \\ 16^{\text {th }} \text { May is Monday } \\ \Rightarrow K=16\end{array}$