Pre-Calculus Honors Unit 6 Lesson 10
Name: _______________________________
Period # _______
Pre-Calculus Honors Unit 6 Lesson 10 Do Now
æ x pö
÷ +1
è 3 4ø
1. Do Now Directions: Sketch and analyze the graph of f (x) = 2 tan ç - +
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
_____________________________________________
æ x pö
÷ +1
è 3 4ø
a.) Find the two corresponding asymptotes of the function f (x) = 2 tan ç - +
b.) Write the three basic points of the parent function, then find the three corresponding
points.
x
x
y = tanx
f (x)
c.) Graph 2 periods of the function on the coordinate plane below.
Pre-Calculus Honors Unit 6 Lesson 10
Book Reference 4.5
Unit 6 Lesson 10: The Graphs of the Secant and Cosecant Function
Objective: ____________________________________________________________________
1. Group Practice: The Graph of y = csc x
1. The graph below represents y = sin x ,  2  x  2 . We are going to use this graph to
see how it relates to the graph of the reciprocal function y = csc x.
2. Complete the table to obtain points on the graph of y = csc x without using a calculator.
You should use the unit circle provided in lesson 6 or lesson 9 to help.
X
0

6

2
5
6

7
6
3
2
11
6
2
y=cscx
3. Use the grid above to sketch the graph of y = csc x in a different color.
4. Compare and contrast the graph of y = csc x and y = sin x. Where do you notice the
vertical asymptotes of the function occur and where the local extrema occur?
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5. Determine the period, the domain, and the range of the cosecant function. You may
write the domain in your own words.
Period
Domain
Range
6. Write a formula, that represents all of the vertical asymptotes of the cosecant function.
________ = _______________ where ________________________________________.
Pre-Calculus Honors Unit 6 Lesson 10
2. Group Practice: The Graph of y = sec x
1. The graph below represents y = cos x ,  2  x  2 . We are going to use this graph to
see how it relates to the graph of the reciprocal function y = sec x.
2. Complete the table to obtain points on the graph of y = sec x without using a calculator.
You should use the unit circle provided in provided in lesson 6 or lesson 9 to help.
x


2


3
0

3

2
2
3

4
3
3
2
5
3
y=secx
3. Use the grid above to sketch the graph of y = sec x in a different color.
4. Compare and contrast the graph of y = sec x and y = cos x. Where do you notice the
vertical asymptotes of the function occur and where the local extrema occur?
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
5. Determine the period, the domain, and the range of the secant function. You may write
the domain in your own words.
Period
Domain
Range
6. Write a formula that represents all of the vertical asymptotes of the secant function.
________ = _______________ where ________________________________________.