Answer
(a) see graph.
(b) $k=5\sqrt 2$ and $\Phi=\frac{\pi}{4}$
Work Step by Step
(a) see graph, we can observe that the graph has the form of a sine curve $y=k\cdot sin(t+\Phi)$
(b) $f(t)=5sin(t)+5cos(t)=5\sqrt 2 (\frac{\sqrt 2}{2}sin(t)+\frac{\sqrt 2}{2}cos(t))=5\sqrt 2 (sin(t)sin\frac{\pi}{4}+cos(t)cos\frac{\pi}{4})=5\sqrt 2 sin(t+\frac{\pi}{4})$ which gives $k=5\sqrt 2$ and $\Phi=\frac{\pi}{4}$
