One of the instructional materials (Slide Presentations) packaged out of the lessons as a result of the study entitled: "INQUIRY-BASED LESSONS IN PRE-CALCULUS FOR SENIOR HIGH SCHOOL"

1. LESSON NO. 7
GRAPHS OF COSECANT
AND
SECANT FUNCTIONS

2. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Topics:
• Graphs of y = csc x and y = sec x
• Graphs of y= a csc bx and y = a sec bx
• Graphs of y = a csc b (x – c) + d and
y = a sec b (x – c) + d

3. Lesson No. 7| Graphs of Cosecant and Secant Functions
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ENGAGE

4. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Engagement Activity 1
Illustrating Cosecant with the Unit Circle
Author:afrewin
Topic:Trigonometry
Reference: https://www.geogebra.org/m/xcVNZQ9G

5. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Illustrating Secant with the Unit Circle
Author:afrewin
Topic:Trigonometry
Reference: https://www.geogebra.org/m/YUJvBfxw#material/NGvteaSQ

6. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Engagement Activity 1
Questions:
1. What is the relationship between the unit Circle
and the cosecant function?
2. What is the relationship between the unit Circle
and the secant function?
3. How will you describe the properties of cosecant
and secant function in terms of the domain and
range?

7. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Engagement Activity 2
Small-Group Interactive Discussion
Graphs of Cosecant & Secant Functions

8. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Small-Group Interactive Discussion on
Graphs of Cosecant & Secant Functions
Inquiry Guide Questions:
• What can you say about the graphs of cosecant and secant functions in
terms of the following:
– Domain;
– Range; and
– Period?
• What is your guide in graphing cosecant and secant functions?
• What are the important properties of the graphs of cosecant and secant
functions?
• Do cosecant and secant functions have amplitude?Why?

9. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Small-Group Interactive Discussion on
Graphs of Cosecant & Secant Functions
Inquiry Guide Questions:
-What are the domains of the cosecant and secant
functions?
-What are the ranges of the cosecant and secant functions?
-What are the periods of the cosecant and secant
functions? What does period mean?
-How do you graph cosecant and secant functions?What
are the things to be considered in graphing the said
functions?

10. Lesson No. 7| Graphs of Cosecant and Secant Functions
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11. Lesson No. 7| Graphs of Cosecant and Secant Functions
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12. Lesson No. 7| Graphs of Cosecant and Secant Functions
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13. Lesson No. 7| Graphs of Cosecant and Secant Functions
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EXPLORE

14. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Explore
• The class will be divided into 8 groups (5-6
members).
• Each group will be given a problem-based task
card to be explored, answered and presented to
the class.
• Inquiry questions from the teacher and learners
will be considered during the explore activity.

15. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Explore
Rubric/Point System of theTask:
0 point – No Answer
1 point – Incorrect Answer/Explanation/Solutions
2 points – Correct Answer but No Explanation/Solutions
3 points – Correct Answer with Explanation/Solutions
4 points – Correct Answer/well-Explained/with
Systematic Solution

16. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Explore
Assigned Role:
Leader – 1 student
Secretary/Recorder – 1 student
Time Keeper – 1
Peacekeeper/Speaker – 1 student
Material Manager – 1-2 students

17. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Explore
Task 1 (Group 1 & Group 2):
Sketch the graph of y =
1
2
csc (x +
𝛱
4
)
Task 2 (Group 3 & Group 4):
Sketch the graph of y = 2 – sec 2x
Task 3 (Group 5 & Group 6):
Sketch the graph of y = 2 csc
𝑥
2
Task 4 (Group 7 & Group 8)
Sketch the graph of y = 3 sec2x

18. Lesson No. 7| Graphs of Cosecant and Secant Functions
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EXPLAIN

19. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Explain
Group Leader/Representative will present the
solutions and answer to the class by
explaining the problem/concept explored
considering the given guide questions.

20. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Explain
Guide Questions:
• What is the problem-based task all about?
• What are the given in the problem-based task?
• What are the things did you consider in
solving/answering the problem-based task?
• What methods did you use in solving/answering
the given problem-based task?

21. Explain
Guide Questions:
- How did you solve/answer the problem-based
task using that method?
- Are there still other ways to answer the
problem/task? How did you do it?
- Are there any limitations to your
solution/answer?
- What particular mathematical concept in
trigonometry did you apply to solve the problem-
based task?
Lesson No. 7| Graphs of Cosecant and Secant Functions
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22. Lesson No. 7| Graphs of Cosecant and Secant Functions
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ELABORATE

23. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Generalization of the Lesson:
• What are the properties of the graphs of
cosecant and secant functions?
• What are the domain and range of cosecant
and secant functions?
• How do we determine the period and phase
shift of cosecant and secant functions?

24. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Elaborate
Integration of Philosophical Views
In this part, the teacher and learners will relate
the term(s)/content/process learned in Lesson 4
about Graphs of Cosecant and Secant Functions in
real life situations/scenario/instances considering
the philosophical views that can be
integrated/associated to term(s)/content/process/
skills of the lesson.

25. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Elaborate
Integration of Philosophical Views
Questions :
• What are the things/situations/instances that you can
relate with regard to the lesson about graphs of cosecant
and secant?
• Considering your philosophical views, how will you relate
the terms/content/process of the lesson in real-life
situations/instances/scenario?

26. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Integration of Philosophical Views
• The graph of sine and cosine function is used as a guide in
graphing cosecant and secant functions. Without a guide,
it is difficult to graph these two functions.
• In the same manner, having a guide in accomplishing the
things in life is very significant because it serves as your
directions towards the achievement of your goals in life.
• This guide works as your blueprint or a framework of the
concepts that you must undertake. At home, you are
guided by your parents on how to behave and act.

27. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Integration of PhilosophicalViews
• In school, your teachers guide you on how to
become excellent students to become a
responsible citizen. At the church, the pastors
and priests lead you in knowing your creator and
finding your purpose in life.
• Having all of them as your guide leads you to the
right path and with them, you can graph a
straight line of your life.

28. Lesson No. 7| Graphs of Cosecant and Secant Functions
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EVALUATE

29. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Evaluate
a) Sketch the graph of the function y = 2 sec
1
2
(x −
𝛱
4
) over
two periods. Find the domain and range of the function.
b) Graph the given cosecant and secant functions with its
period, and phase shift and determine its domain & range.
i) y = 2csc (x) + 1
ii) y = − 2sec (x −
𝛱
2
) – 3

30. Evaluate
c) Compare and contrasts the graphs of
y = −3 sec x and y = −sec 3 x.
d) How does the graph of y = -csc x is
similar/different from the graph of y = csc (-
x)?
Lesson No. 7| Graphs of Cosecant and Secant Functions
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31. Lesson No. 7| Graphs of Cosecant and Secant Functions
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Assignment:
Answer the following questions:
1.What is the difference between tangent and cotangent
graphs?
2. How do we graph tangent and cotangent functions?
3.What are the domain, range & period of tangent &
cotangent functions?
Reference: DepED Pre-Calculus Learner’s Material, pages 158 – 160
-GNDMJR-