Answer: (b) \(5\); (c) \(4\pi\), or \(720^\circ\).

Answer: (b) \(5\); (c) \(4\pi\), or \(720^\circ\).

(a) The graph

\(y=5\sin\frac{x}{2}+1\)

has midline \(y=1\), amplitude \(5\), maximum value \(6\), and minimum value \(-4\).

Since the coefficient of \(x\) is \(\frac12\), the period is

\(\frac{2\pi}{1/2}=4\pi.\)

On the interval \(-2\pi\leq x\leq2\pi\), the key points are

\((-2\pi,1),\quad (-\pi,-4),\quad (0,1),\quad (\pi,6),\quad (2\pi,1).\)

These points give one complete sine cycle.

(b) The amplitude is \(5\).

(c) The period is \(4\pi\).