5 A curve is defined by the parametric equations \(x = \cos 2 t , y = \sin t\).
The point \(P\) on the curve is where \(t = \frac { \pi } { 6 }\).
- Find the gradient at \(P\).
- Find the equation of the normal to the curve at \(P\) in the form \(y = m x + c\).
- The normal at \(P\) intersects the curve again at the point \(Q ( \cos 2 q , \sin q )\).
Use the equation of the normal to form a quadratic equation in \(\sin q\) and hence find the \(x\)-coordinate of \(Q\).
[0pt]
[5 marks]