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Let \(f(x) = 6 + 6\,sin\,x\).

Part of the graph of \(f\) is shown below.

The figure is not to scale.

The shaded region is bounded by the curve of \(f\), the x-axis and the y-axis.

The path makes an angle of \(4^\circ\) with the horizontal.

1. Solve, for \(0 \leq x \leq 2\pi\)
   1. \(6 + 6\,sin\,x = 6\).
   2. \(6 + 6\,sin\,x = 0\).
2. Write down the exact value of the x-intercept of \(f\), for \(0 \leq x \leq 2\pi\).
3. The area of the shaded region is \(k\). Find the value of \(k\), giving your answer in terms of \(\pi\).

Let \(g(x) = 6 + 6\,sin\,(x - \frac{\pi}{2})\). The graph of \(f\) is transformed to that of \(g\).

4. Give a full geometric description of this transformation.
5. Given that \(\int_p^{p+\frac{3\pi}{2}}g(x)\,dx = k\) and \(0 \leq p < 2\pi\), write down the two values of \(p\).