$($b$)$ The graph of a trigonometric function $y=f(x),$ where $x$ is in degrees, is shown below. The coordinates of the points A and $B$ are $(-30,-1)$ and $(15,2)$ respectively, and $B$ lies on the midway line.

$($i$)$ Find the coordinates of the points $C$ and $D.$

$($ii$)$ Write the amplitude and the period of the function above.

$($ii$)$ Write the equation of the graph.