Read graph parameters (a, b, c)

4
\includegraphics[max width=\textwidth, alt={}, center]{80a20f05-61db-42d9-b4ba-53eea2290b2d-05_677_1591_260_278} The diagram shows part of the graph of \(y = a \tan ( x - b ) + c\).
Given that \(0 < b < \pi\), state the values of the constants \(a , b\) and \(c\).

2
\includegraphics[max width=\textwidth, alt={}, center]{89a18f20-a4d6-4a42-8b00-849f4fb89692-04_657_1253_269_431} The diagram shows part of the curve with equation \(y = p \sin ( q \theta ) + r\), where \(p , q\) and \(r\) are constants.

1. State the value of \(p\).
2. State the value of \(q\).
3. State the value of \(r\).

1
\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.

1. State the values of \(a , b\) and \(c\).
2. 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:
   1. \(a \sin ( b x ) + c = 7 - x\)
   2. \(\quad a \sin ( b x ) + c = 2 \pi ( x - 1 )\).

4
\includegraphics[max width=\textwidth, alt={}, center]{3b527397-7781-41e9-8218-57277cc977bf-2_561_1210_895_465} The diagram shows the graph of \(y = a \sin ( b x ) + c\) for \(0 \leqslant x \leqslant 2 \pi\).

1. Find the values of \(a , b\) and \(c\).
2. Find the smallest value of \(x\) in the interval \(0 \leqslant x \leqslant 2 \pi\) for which \(y = 0\).

1
\includegraphics[max width=\textwidth, alt={}, center]{62f7f1e2-a8e7-4574-a432-8e9b20b54d7a-2_750_1287_258_427} The diagram shows part of the graph of \(y = a + b \sin x\). State the values of the constants \(a\) and \(b\). [2

2 The curves in parts (i) and (ii) have equations of the form \(y = a + b \sin c x\), where \(a , b\) and \(c\) are constants. For each curve, find the values of \(a , b\) and \(c\).

1. 
   \includegraphics[max width=\textwidth, alt={}, center]{11877196-83d9-4283-9eef-e617bea50c63-1_449_681_834_408}
2. 
   \includegraphics[max width=\textwidth, alt={}, center]{11877196-83d9-4283-9eef-e617bea50c63-1_376_681_1344_408}

5 The curves in parts (i) and (ii) have equations of the form \(y = a + b \sin c x\), where \(a , b\) and \(c\) are constants. For each curve, find the values of \(a , b\) and \(c\).

1. 
   \includegraphics[max width=\textwidth, alt={}, center]{3b3e20ee-457c-46be-b2e5-12573bee2fbf-2_455_679_1800_365}
2. 
   \includegraphics[max width=\textwidth, alt={}, center]{3b3e20ee-457c-46be-b2e5-12573bee2fbf-2_374_679_2311_365}