8 The equation of a curve, in polar coordinates, is
$$r = 1 + \cos 2 \theta , \quad \text { for } 0 \leqslant \theta < 2 \pi$$
- State the greatest value of \(r\) and the corresponding values of \(\theta\).
- Find the equations of the tangents at the pole.
- Find the exact area enclosed by the curve and the lines \(\theta = 0\) and \(\theta = \frac { 1 } { 2 } \pi\).
- Find, in simplified form, the cartesian equation of the curve.