The equation of the curve is given by \(y = p \sin(q\theta) + r\).

(a) The amplitude of the sine function is the coefficient \(p\). From the graph, the maximum value is 1 and the minimum value is -5, giving an amplitude of \(\frac{1 - (-5)}{2} = 3\). Thus, \(p = 3\).

(b) The period of the sine function is given by \(\frac{2\pi}{q}\). From the graph, the period is \(4\pi\), so \(\frac{2\pi}{q} = 4\pi\). Solving for \(q\), we get \(q = \frac{1}{2}\).

(c) The vertical shift \(r\) is the average of the maximum and minimum values of the function. Thus, \(r = \frac{1 + (-5)}{2} = -2\).