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
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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