Trigonometry - Trigonometric Graphs and Parameters

The diagram shows the graphs of \(y = 3 \cos 2x\) and \(y = k - \cos x\) for \(0 \le x \le \frac{5\pi}{4}\). The curves have a common maximum point \(Q\). Find

1. the value of \(k\),
2. the coordinates of \(Q\), and
3. the coordinates of the next common maximum point of the two curves (in the positive \(x\)-direction).