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Section 6 - Graphs of Other Trig Functions

Page history last edited by PBworks 16 years, 2 months ago

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 eq=\pi (not 2eq=\pi)

 

 

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:  eq=\frac{\pi}{b}

 

horizontal shifteq=\frac{c}{b}  (goes opposite direction of the sign)

 

vertical shift:  d

 

 

 

Example

 

eq=y=3tan(2x-\pi)-2

 

amplitude: none

period: Formula

hs: Formula (right)

vs: -2

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

 

 

 

 

Other Trig Graphs

 

 

 

y = csc x                                 

 

 

 

 

 

y = sec x                       

 

 

 

 

 

y = cot x                        

 

 

Comments (1)

Anonymous said

at 8:38 pm on Jan 8, 2008

I think this is the best wiki page ever invented. Seriously.

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