NAME:
PERIOD:
NOTES
ALGEBRA II H
Asymptotes
OBJECTIVE
DATE:
Graphs of secant and cosecant functions
Warm up: Example #1: Find the value of the following reciprocal trigonometric functions.
a)
=
b)
( )
=
( )
c)
=
( )
d)
=
Graphs of secant and cosecant functions: The graphs of trigonometric functions
=
( )
and
=
can be obtained from the graphs of the sine and cosine functions using the reciprocal identities.
=
=
Step 1: Draw a graph of its reciprocal function. For instance, to sketch the graph of
the graph of
=
=
, first sketch
.
Step 2: Then take reciprocals of the y-coordinates to obtain points on the graph of
=
. Additionally,
x-intercepts of the sine and cosine functions become vertical asymptotes of the cosecant and secant
functions.
Example #2: Draw the graph of
=
.
Example #3: Draw the graph of
=
.
Example #4: Draw the graph of
= 4 sec(2
Example #5: Draw the graph of
=
3 csc(
).
).