- A curve \(C\) has equation
$$y = 3 \sin 2 x + 4 \cos 2 x , - \pi \leqslant x \leqslant \pi$$
The point \(A ( 0,4 )\) lies on \(C\).
- Find an equation of the normal to the curve \(C\) at \(A\).
- Express \(y\) in the form \(R \sin ( 2 x + \alpha )\), where \(R > 0\) and \(0 < \alpha < \frac { \pi } { 2 }\).
Give the value of \(\alpha\) to 3 significant figures.
- Find the coordinates of the points of intersection of the curve \(C\) with the \(x\)-axis. Give your answers to 2 decimal places.