$\"\"$

The trigonometric function is $\"\"$ .

Recriprocal identity: $\"\"$ .

Hence consider the function $\"\"$ .

First graph the function $\"\"$ .

Compare the function $\"\"$ with $\"\"$ .

Here $\"\"$ .

Amplitude: $\"\"$ .

Period: $\"\"$ .

$\"\"$

Solve the equations for the interval $\"\"$ .

$\"\"$ and $\"\"$ .

The interval $\"\"$ corresponds to one cycle of the graph.

Divide the interval into four equal parts to produce the key points.

Construct the table of values in the interval $\"\"$ :

\ \

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

$\"\"$

Graph :

1. Draw a coordinate plane.

2. Plot the points and sketch the asymptotes.

3.Connect the points with a smooth curve.

4.Repeat the same pattern for the next cycles.

$\"\"$

Observe the graph:

The function $\"\"$ has vertical asyptotes at $\"\"$ , $\"\"$ and $\"\"$ .

The domain of the function is $\"\"$ .

The range of the function is $\"\"$ .

$\"\"$

The graph of $\"\"$ is

$\"\"$

The domain of the function is $\"\"$ .

The range of the function is $\"\"$ .