Graphs of a cosine and its scaled reciprocal secant, with asymptotes and counts of solutions

The function \(\mathrm{f}\) is given by \(\mathrm{f}(x)=3\sec3x\) for \(0\le x\le\pi\).

1. Sketch the graph of \(y=\cos3x\) for \(0\le x\le\pi\).[2]
2. On the same diagram, sketch the graph of \(y=\mathrm{f}(x)\), showing the equation of each vertical asymptote.[3]
3. Write down the smallest positive value of \(x\) for which \(\mathrm{f}(x)=-3\).[2]
4. Find the number of solutions of the equation \(\left|\mathrm{f}(x)\right|=4\) for \(0\le x\le\pi\).[2]