1.1. The graph of the curve C shown below is defined by the parametric equations

$x=2cos3 \theta$    $y=5sin \theta$     $0\leq \theta \leq2 \pi$

Find an expression for  $\frac{dy}{dx}$  in terms of  $\theta$.

1.2. (i) Show that the gradient of the tangent to C, at the point where  $\theta =\frac{ \pi }{4}$,  is  $-\frac{5}{6}$ .

(ii) Hence find the equation of the tangent to C at the point where  $\theta =\frac{ \pi }{4}$ .