Trigonometry - Trigonometric Graphs and Parameters

The function \(f\) is defined, for all values of \(x\), by \(f(x) = a \sin x + c\), where \(a\) and \(c\) are constants and \(a < 0\).

1. Given that the graph of \(y = f(x)\) passes through the points \((0, -1)\) and the maximum value of \(y\) is \(4\), find the values of \(a\) and \(c\).
2. Sketch the graph of \(y = f(x)\) for \(0 \leq x \leq 5\pi\).
3. Given that when \(x = \frac{\pi}{6}\), \(y = -\frac{7}{2}\), find all other values of \(x\) between \(0\) and \(5\pi\) for which \(y = -\frac{7}{2} .\)