6 A curve is given by the parametric equations
$$x = \cos \theta \quad y = \sin 2 \theta$$
- Find \(\frac { \mathrm { d } x } { \mathrm {~d} \theta }\) and \(\frac { \mathrm { d } y } { \mathrm {~d} \theta }\).
(2 marks) - Find the gradient of the curve at the point where \(\theta = \frac { \pi } { 6 }\).
- Show that the cartesian equation of the curve can be written as
$$y ^ { 2 } = k x ^ { 2 } \left( 1 - x ^ { 2 } \right)$$
where \(k\) is an integer.