Lesson no. 7 (Graphs of Cosecant and Secant functions)

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 _____________________________________________________________________ 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 _____________________________________________________________________ ENGAGE

4. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________1 Engagement Activity 2 Small-Group Interactive Discussion Graphs of Cosecant & Secant Functions

8. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________

11. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________

12. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________

13. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ EXPLORE

14. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ 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 _____________________________________________________________________ Explore Rubric/Point System of the Task : 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 _____________________________________________________________________ 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 _____________________________________________________________________ Explore   Task 1 (Group 1 & Group 2): Sketch the graph of y = csc (x +   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   Task 4 (Group 7 & Group 8) Sketch the graph of y = 3 sec2x  

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

19. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________

22. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ ELABORATE

23. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________ 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 _____________________________________________________________________ Integration of Philosophical Views 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 _____________________________________________________________________ EVALUATE

29. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ Evaluate a) Sketch the graph of the function y = 2 sec (x − ) 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 − ) – 3  

30. Evaluate c ) Compare and contrasts the graphs of y = sec x and y = sec 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 _____________________________________________________________________

31. Lesson No. 7| Graphs of Cosecant and Secant Functions _____________________________________________________________________ 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-