Graphs of Other Trig Functions

 

 

Since we've already learned how to graph sin x and cos x (see 4.5), we need to look at the graphs of y = tan x and all the other reciprocal functions.

 

First, graph y = tan x using ordered pairs.  Choose easy angles for x to find the tangent of.

x	y
0	0
90	undef.
180	0
270	undef
360	0
45	1

 

**Any undefined y value means that there is an asymptote on the graph.

 

Note the differences between tangent and the sine and cosine graphs that we've already done:

1. there is no amplitude (tangent goes on forever!)

2. the period is  (not 2)

 

 

To graph:

1. Plot the center point of the curve (normally at the origin unless there's a horizontal or vertical shift)

2. Cut the period in half - put half on the right of the point (label axis), half on the left of the point (label axis); these are the locations of the asymptotes

3. Draw the curve (it looks like a cubic)

 

 

 

How do you find amplitude, period, horizontal shift, and vertical shift?

 

The basic equation is y = a tan (bx + c) + d

 

amplitude:  none (remember, amplitude is the height of the curve;  tangent goes up forever!)

 

period: 

 

horizontal shift:    (goes opposite direction of the sign)

 

vertical shift:  d

 

 

 

Example

 

 

amplitude: none

period:

hs:  (right)

vs: -2

Graph goes through point (, -2), asymptotes are right and  left

 

 

 

 

Other Trig Graphs

 

 

 

y = csc x                                 

 

 

 

 

 

y = sec x                       

 

 

 

 

 

y = cot x