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-

3. Trig Values in Coordinate Planey
Quadrant II
Quadrant I
function
reciprocal
function
reciprocal
cos  is –
sin  is +
tan  is –
sec  is –
csc  is +
cot  is –
cos  is +
sin  is +
tan  is +
sec  is +
csc  is +
cot  is + x
Quadrant III
Quadrant IV
cos  is –
sin  is –
tan  is +
sec  is –
csc  is –
cot  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
|a| = amplitude (vertical stretch or shrink)
h = phase shift, or horizontal shift
k = vertical shift
|b| = frequency
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