Find the value of \(p\), the value of \(m\) and the value of \(n\).
Show that the equation of \(C\) can be written in the form \(y = r + \mathrm { f } ( x - h )\) and specify the function f and the constants \(r\) and \(h\).
The region bounded by \(C\), the \(x\)-axis and the lines \(x = \frac { \pi } { 6 }\) and \(x = \frac { \pi } { 3 }\) is rotated through \(2 \pi\) radians about the \(x\)-axis.