- The curve \(C\) has polar equation \(r = 3 ( 2 + \cos \theta ) , 0 \leq \theta \leq \pi\). Determine the area enclosed between \(C\) and the initial line. Give your answer in the form \(\frac { a } { b } \pi\), where \(a\) and \(b\) are positive integers whose values are to be found.
- Find the three cube roots of the complex number \(2 + 3 \mathrm { i }\), giving your answers in Cartesian form.
- Find all the roots of the equation
$$\cos \theta + \cos 3 \theta + \cos 5 \theta = 0$$
lying in the interval \([ 0 , \pi ]\). Give all the roots in radians in terms of \(\pi\).