Question 3
Let $A(2,0)$ be fixed in the plane and let $P(\sin(2t-60^\circ),\cos(2t-60^\circ))$ move as $t$ varies from $15^\circ$ to $45^\circ$. If the area swept out by the segment $AP$ is $S$, find $\lfloor100S\rfloor$. (The source also calls the area $A$; here $S$ avoids confusion with the point.)