Express \(\sin 2 \theta\) and \(\cos 2 \theta\) in terms of \(\sin \theta\) and \(\cos \theta\).
Given that \(0 < \theta < \frac { \pi } { 2 }\) and \(\cos \theta = \frac { 3 } { 5 }\), show that \(\sin 2 \theta = \frac { 24 } { 25 }\) and find the value of \(\cos 2 \theta\).
A curve has parametric equations
$$x = 3 \sin 2 \theta , \quad y = 4 \cos 2 \theta$$
Find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) in terms of \(\theta\).
At the point \(P\) on the curve, \(\cos \theta = \frac { 3 } { 5 }\) and \(0 < \theta < \frac { \pi } { 2 }\). Find an equation of the tangent to the curve at the point \(P\).