IB Math HL Trigonometry Test 3 2014 P1 Q6

Consider \(f(x)=2\sec4x\), \(0\le x\le\pi\).

1. Sketch \(y=\cos4x\) for \(0\le x\le\pi\).[2]
2. On the same diagram sketch \(y=f(x)\), indicating all asymptotes.[3]
3. Write down the smallest positive solution of \(f(x)=-2\).[2]
4. Find the number of solutions of \(|f(x)|=e\) for \(0\le x\le\pi\).[2]