- In this question you must show all stages of your working.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
The curve \(C\) has parametric equations
$$x = \sin t - 3 \cos ^ { 2 } t \quad y = 3 \sin t + 2 \cos t \quad 0 \leqslant t \leqslant 5$$
- Show that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = 3\) where \(t = \pi\)
The point \(P\) lies on \(C\) where \(t = \pi\)
- Find the equation of the tangent to the curve at \(P\) in the form \(y = m x + c\) where \(m\) and \(c\) are constants to be found.
Given that the tangent to the curve at \(P\) cuts \(C\) at the point \(Q\)
- show that the value of \(t\) at point \(Q\) satisfies the equation
$$9 \cos ^ { 2 } t + 2 \cos t - 7 = 0$$
- Hence find the exact value of the \(y\) coordinate of \(Q\)