Aim: How can we graph the reciprocal trig functions using the three basic trig ones?

1
Aim How can we graph the reciprocal trig
functions using the three basic trig ones?
Do Now
In the diagram below of right triangle JMT, JT
12, JM 6 and m?JMT 90. What is the value of
cot J?
J
M
T
2
Reciprocal Identities
Co-
Co-
Co-
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Trig Values in Coordinate Plane
y
Quadrant I
Quadrant II
sec ? is csc ? is cot ? is
cos ? is sin ? is tan ? is
cos ? is sin ? is tan ? is
sec ? is csc ? is cot ? is
x
Quadrant IV
Quadrant III
sec ? is csc ? is cot ? is
cos ? is sin ? is tan ? is
cos ? is sin ? is tan ? is
sec ? is csc ? is cot ? is
For any given angle, a trig function and
its reciprocal have values with the same sign.
4
Reciprocals Graph of Cosecant
reciprocal of 0
- undefined
therefore
these are the only points of equality
f(x) csc x
5
Reciprocals Graph of Secant
reciprocal of 0
undefined
therefore
these are the only points of equality
f(x) sec x
6
Reciprocals Graph of Cotangent
the only points of equality
f(x) cot x
-?
7
Model Problems
Which expression represents the exact value of
csc 60o?
Which expression gives the correct values of csc
60o?
Which is NOT an element of the domain of y cot
x?
8
Model Problems
A handler of a parade balloon holds a line of
length y. The length is modeled by the function
y d sec ?, where d is the distance from the
handler of the balloon to the point on the ground
just below the balloon, and ? is the angle formed
by the line and the ground. Graph the function
with d 6 and find the length of the line needed
to form an angle of 60o.
9
Model Problem
Graph the function
dilation frequency phase shift vertical shift
a 2
b 3
k -2
10
Model Problem
Graph the function
dilation frequency phase shift vertical shift
a 2
b 3
k -2