On the same axes, sketch the graphs of \(y = \cos x\) and \(y = \cos 2 x\) for values of \(x\) from 0 to \(2 \pi\).
Describe the transformation which maps the graph of \(y = \cos x\) onto the graph of \(y = 3 \cos x\).
\(4 \theta\) is an acute angle and \(\sin \theta = \frac { 1 } { 4 }\). Find the exact value of \(\tan \theta\).