Zadanie 9e, Paper 2, listopad 2024, TZ1, Matematyka AA IB SL

All trigonometric arguments are in radians. Let $f(x)=5\sin(3\pi x)$ and $g(x)=-12\cos(3\pi x)$. Their sum can be written $a\cos(b(x-c))$ with a,b,c>0. In a separate motion model, a conveyor carries a scanner along a straight track with velocity $v(t)=6+2\sin(\pi(t-3)/12)$ metres per second for t≥0 seconds. Identical inspection checkpoints occur whenever the scanner reaches its maximum velocity. The scanner keeps moving forward.