Pre-Calculus Honors Unit 6 Lesson 9
Name: _______________________________
Period # _______
Pre-Calculus Honors Unit 6 Lesson 9 Do Now
æx p ö
÷ -1
è3 4ø
1. Do Now Directions: Sketch and analyze the graph of f (x) = -tan ç +
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æx p ö
÷ -1
è3 4ø
a.) Find two asymptotes of the function f (x) = -tan ç +
b.) Write the three basic points of the graph, 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 9
Book Reference 4.5
Unit 6 Lesson 9: 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 8 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 an equation, or formula, that represents all of the vertical asymptotes of the
cosecant function.
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Pre-Calculus Honors Unit 6 Lesson 9
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 8 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?
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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 an equation, or formula, that represents all of the vertical asymptotes of the secant
function.
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Pre-Calculus Honors Homework: Pg 439 Review Problems #(55 - 58)