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\includegraphics[max width=\textwidth, alt={}, center]{39393c20-34df-4167-a8bf-e4067371de81-02_778_1195_260_475}
The diagram shows the curve with equation \(y = a \sin ( b x ) + c\) for \(0 \leqslant x \leqslant 2 \pi\), where \(a , b\) and \(c\) are positive constants.
- State the values of \(a , b\) and \(c\).
- For these values of \(a , b\) and \(c\), determine the number of solutions in the interval \(0 \leqslant x \leqslant 2 \pi\) for each of the following equations:
- \(a \sin ( b x ) + c = 7 - x\)
- \(\quad a \sin ( b x ) + c = 2 \pi ( x - 1 )\).