The trigonometric function is .

Compare the above function with .

.

The period is . 

The factor of will shrink the graph of horizontally by making all the y - coordinates four times larger.

The factor of is the all of the y-coordinates of and x-axis reflection.

There is a coefficient of 3 in the argument.

The period of the cosecant function is .

One cycle :

.

The period is , and divide the period by 4, then resuilt is , mark the x - axis in increments of starting at .

0, , , , and . 

1). Draw a coordinate plane.

2). Sketch a frame to help plot the key points and draw the asymptotes.

3). The difference is that the upper and lower sides of the frame do not indicate maximum and minimum values of the graph but are only used to define the position of two key points.

4). The graph of the trigonometric function is :

The graph of the trigonometric function is :