Operation Manual

Applications 14-11
8214APPS.DOC TI-82, Chapter 14, English Bob Fedorisko Revised: 02/09/01 9:27 AM Printed:
02/09/01 12:43 PM Page 11 of 20
The Unit Circle and Trigonometric Curves
You can use the parametric graphing feature of the TI
.
82 to show the relationship
between the unit circle and any trigonometric curve.
Problem
Graph the unit circle and the sine curve to demonstrate graphically the
relationship between them.
Any function that can be plotted in function graphing can be plotted in
parametric graphing by defining the
X
component as
T
and the
Y
component as F(
T
).
Solution
1. Press
z
. Select
Radian
,
Par
, and
Simul
.
2. Press
p
. Set the viewing
WINDOW
.
Tmin = 0 Xmin =
M
2 Ymin =
M
3
Tmax = 2
p
Xmax = 2
p
Ymax = 3
Tstep = .1 Xscl =
pà
2 Yscl = 1
3. Press
o
. Turn off all selected functions. Enter the expressions to
define the unit circle centered at (
L
1,0).
X
1T
=cos T–1
Y
1T
=sin T
4. Enter the expressions to define the sine curve.
X
2T
=T
Y
2T
=sin T
5. Press
r
. As the graph is plotting, you may press
Í
to pause and
resume graphing as you watch the sine function “unwrap” from the unit
circle.
Note: The “unwrapping” can be generalized. Replace
sin T
in
Y
2T
with any
other trig function to “unwrap” that function.