1. Graphs of Other Trigonometric Functions
Section 4.6

2. Graph of the Tangent Function
To graph y = tan x, use the identity
At values of x for which cos x = 0, the tangent function is undefined and its graph has vertical asymptotes. y x
Properties of y = tan x
1. domain : all real x
2. range: (–, +)
3. period: 
4. vertical asymptotes:
period:

3. Steps in Graphing y = a tan bx.
1. Determine the period
2. Locate two adjacent vertical asymptotes by solving for x:
3. Sketch the two vertical asymptotes found in Step 2.
4. Divide the interval into four equal parts.
5. Evaluate the function for the first – quarter point, midpoint, and third - quarter point, using the x – values in Step 4.
6. Join the points with a smooth curve, approaching the vertical asymptotes. Indicate additional asymptotes and periods of the graph as necessary.

4. Example: Find the period and asymptotes and sketch the graph of
1. Period of y = tan x is  .
2. Find consecutive vertical
asymptotes by solving for x:
Vertical asymptotes:
3. Plot several points in
4. Sketch one branch
and repeat.

5. Example: Find the period and asymptotes and sketch the graph of
1. Period of y = tan x is of
Period is
2. Find consecutive vertical
asymptotes by solving for x:
Vertical asymptotes:
3. Divide - to  into four
equal parts.
4. Sketch one branch and
repeat.

6. Graph 1. Period is or 4. 2. Vertical asymptotes are
x = - 2
x = 2 y x
Graph
1. Period is or 4.
2. Vertical asymptotes are
3. Divide the interval - 2 to 2 into four equal parts.