The graph of \(y = a \sin bx + c\) has a turning point at \(\left(\frac{\pi}{4}, 0\right)\) and the next turning point after this has coordinates \(\left(\frac{3\pi}{4}, 6\right)\).
Find the values of the constants \(a\), \(b\) and \(c\).[3]
Hence, sketch the graph of \(y = a \sin bx + c\) for \(0 \le x \le 2\pi\).[2]
By drawing a suitable straight line on the same axes, find the number of solutions of the equation \(a \sin bx = -\frac{3}{2\pi}x\).[3]
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