- A curve \(C\) has parametric equations
$$x = 2 \sin t , \quad y = 1 - \cos 2 t , \quad - \frac { \pi } { 2 } \leqslant t \leqslant \frac { \pi } { 2 }$$
- Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) at the point where \(t = \frac { \pi } { 6 }\)
- Find a cartesian equation for \(C\) in the form
$$y = \mathrm { f } ( x ) , \quad - k \leqslant x \leqslant k$$
stating the value of the constant \(k\).
- Write down the range of \(\mathrm { f } ( x )\).