\begin{align*} \text{Center line: } & y = 0 \\ c & = 0 \\ \\ \text{Amplitude} & = 3 \\ a & = 3 \\ \\ \text{Period} & = 180^\circ \\ {360^\circ \over b} & = 180^\circ \\ 360^\circ & = (180^\circ) b \\ {360^\circ \over 180^\circ} & = b \\ 2 & = b \\ \\ \\ \therefore a = 3, b = 2, c = 0 \end{align*}

\begin{align*} \text{Center line: } & y = 2 \\ c & = 2 \\ \\ \text{Amplitude} & = 2 \\ a & = -2 \phantom{000000} [\text{Due to inverted shape}] \\ \\ \text{Period} & = {\pi \over 2} \\ {2\pi \over b} & = {\pi \over 2} \\ 2(2\pi) & = \pi b \\ 4\pi & = \pi b \\ {4\pi \over \pi} & = b \\ 4 & = b \\ \\ \\ \therefore a = -2, b & = 4, c = 2 \end{align*}

\begin{align} \text{Center line: } & y = 3 - 4 \\ & y = -1 \\ \\ c & = -1 \\ \\ \text{Amplitude} & = 4 \\ a & = 4 \\ \\ \text{Period} & = 720^\circ \\ {360^\circ \over {1 \over b}} & = 720^\circ \\ 360 b & = 720 \\ b & = {720 \over 360} \\ b & = 2 \\ \\ \\ \therefore a = 4, b & = 2, c = -1 \end{align}

\begin{align*} y & = - \cos \left({x \over 2}\right) - 1 \\ y & = - \cos \left({1 \over 2}x\right) - 1 \phantom{000000} [\text{Inverted shape}] \\ y & = - \cos (0.5 x) - 1 \\ \\ \text{Amplitude} & = 1 \\ \\ \text{Center line: } & y = -1 \\ \\ \text{Maximum value} & = -1 + 1 \\ & = 0 \\ \\ \text{Minimum value} & = -1 - 1 \\ & = -2 \\ \\ \text{Period} & = {2\pi \over 0.5} \\ & = 4 \pi \\ \\ \text{No. of cycles} & = {6\pi \over 4\pi} \\ & = 1{1 \over 2} \end{align*}

\begin{align} \text{Period} & = \pi \\ \\ m & = k + \pi \end{align}

\begin{align} k + l & = {\pi \over 2} \end{align}

\begin{align} y & = 2 \cos 2x \\ \\ \text{Amplitude} & = 2 \\ \\ \text{Max. value} & = 2 \\ \text{Min. value} & = -2 \\ \\ \text{Period} & = {2\pi \over 2} \\ & = \pi \\ \\ \text{No. of cycles} & = {2\pi \over \pi} \\ & = 2 \\ \\ \\ y & = \sin x + 1 \\ \\ \text{Amplitude} & = 1 \\ \\ \text{Center line: } & y = 1 \\ \\ \text{Max. value} & = 1 + 1 = 2 \\ \text{Min. value} & = 1 - 1 = 0 \\ \\ \text{Period} & = {2\pi \over 1 }\\ & = 2\pi \\ \\ \text{No. of cycles} & = {2\pi \over 2\pi} \\ & = 1 \end{align}