\begin{align} \text{Center line: } & y = 1 \\ c & = 1 \\ \\ \text{Amplitude} & = 2 \\ a & = 2 \\ \\ \text{Period} & = 180^\circ \\ {360^\circ \over b} & = 180^\circ \\ 360 & = 180b \\ {360 \over 180} & = b \\ 2 & = b \\ \\ \\ \therefore a = 2, b & = 2, c = 1 \end{align}

\begin{align*} \text{Center line: } & y = 0 \\ c & = 0 \\ \\ \text{Amplitude} & = 2 \\ a & = -2 \\ \\ \text{Period} & = \pi \\ {2\pi \over b} & = \pi \\ 2\pi & = \pi b \\ 2 & = b \\ \\ \\ \therefore a = -2, b & = 2, c = 0 \end{align*}

\begin{align} y & = a \sin x + b \\ \\ \text{Center line: } y & = {5 + (-9) \over 2} \\ y & = -2 \\ \\ \text{Amplitude} & = 5 - (-2) \\ & = 7 \\ \\ \therefore a & = \pm 7, b = -2 \end{align}

\begin{align*} y & = 2 \sin {\pi x \over 3} + 3 \\ y & = 2 \sin \left({\pi \over 3} x \right) + 3 \phantom{000000}[ y = a \sin bx + c] \\ \\ \text{Amplitude} & = 2 \\ \\ \text{Center line: } & y = 3 \\ \\ \text{Max. value} & = 3 + 2 = 5 \\ \text{Min. value} & = 3 - 2 = 1 \\ \\ \text{Period} & = {2\pi \over {\pi \over 3}} \phantom{0000000000000000} [\text{Note } x \text{ is in radians}] \\ & = 2\pi \div {\pi \over 3} \\ & = {2\pi \over 1} \times {3 \over \pi} \\ & = {6 \pi \over \pi} \\ & = 6 \end{align*}

\begin{align*} y & = 3 \sin 2x \\ \\ \text{Amplitude} & = 3 \\ \text{Max. value} & = 3 \\ \text{Min. value} & = -3 \\ \\ \text{Period} & = {2\pi \over 2} = \pi \\ \\ \\ y & = 3 - {2x \over \pi} \\ y & = 3 - {2 \over \pi} x \\ y & = - {2 \over \pi} x + 3 \phantom{000000} [\text{Straight line } y = mx + c] \\ \\ \text{Let } & x = 0, \\ y & = -{2 \over \pi} (0) + 3 \\ y & = 3 \phantom{00000000000000} [y \text{-intercept}] \\ \\ \text{Let } & y = 0, \\ 0 & = -{2 \over \pi} x + 3 \\ {2 \over \pi} x & = 3 \\ 2x & = 3 \pi \\ x & = {3\pi \over 2} \phantom{000000000000.} [x \text{-intercept}] \end{align*}