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. 5
REFERENCE ANGLE

2. Lesson No. 5 |Reference Angle
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ENGAGE

3. Lesson No. 5 |Reference Angle
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Engagement Activity
Investigating Reference Angle
Author: Scott Farrar
Topic:Angles,Triangles
Reference: http://www.geogebra.org
Drag P.

4. Lesson No. 5 |Reference Angle
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Engagement Activity
Questions:
1.What is a reference angle?
2.What is the use of a reference angle?
3. How do we find a reference angle?

5. Lesson No. 5 |Reference Angle
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Small-Group Interactive Discussion
Reference Angle

6. Lesson No. 5 |Reference Angle
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Small-Group Interactive Discussion
on Reference Angle
Inquiry Guide Questions:
- What can you observe about the values of
the six circular or trigonometric functions at
θ1 and θ2 if the given two angles are
coterminal?
- Based on your observation, how do we find
the value of a circular function at a number
θ?

7. Lesson No. 5 |Reference Angle
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Small-Group Interactive Discussion
on Reference Angle
Inquiry Guide Questions:
- How do we determine the value of a
particular circular function at an angle θ
considering the correct sign? How do we
determine the correct sign?
- Where does the sign of the coordinates of
P(θ) depends?

8. Lesson No. 5 |Reference Angle
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EXPLORE

9. Lesson No. 5 |Reference Angle
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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 exploration activity.

10. Lesson No. 5 |Reference Angle
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Explore
Rubric/Point System of theTask:
0 point – No Answer
1 point – IncorrectAnswer/Explanation/Solutions
2 points – CorrectAnswer but No Explanation/Solutions
3 points – Correct Answer with Explanation/Solutions
4 points – Correct Answer/well-Explained/with
Systematic Solution

11. Lesson No. 5 |Reference Angle
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Explore
Assigned Role:
Leader – 1 student
Peacekeeper/Speaker – 1 student
Secretary/Recorder – 1 student
Time Keeper – 1
Material Manager – 1-2 students

12. Lesson No. 5 |Reference Angle
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Explore
• Problem 1 (Group 1 & Group 2):
Use reference angle and appropriate sign to find the
exact value of each expression
a) sin 150° b) sin
11𝜋
6
and cos
11𝜋
6
• Problem 2 (Group 3 & Group4):
Find the exact value of each expression using reference
angle & appropriate sign.
a) cos (−
11𝜋
6
) b) tan
8𝜋
3
and cot
8𝜋
3

13. Lesson No. 5 |Reference Angle
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Explore
• Problem 3 (Group 5 & Group 6):
Find the six trigonometric functions of the angle θ if
the terminal side of θ in standard position passes
through (5, -12)
• Problem 4 (Group 7 & Group 8):
If P(θ) is a point on the unit circle and θ =
5𝜋
6
, find
the values of the six trigonometric functions of θ.

14. Lesson No. 5 |Reference Angle
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EXPLAIN

15. Lesson No. 5 |Reference Angle
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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 following
questions

16. Lesson No. 5 |Reference Angle
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Explain
Guide Questions:
 What is the problem all about?
 What are the given in the problem?
 What are the things did you consider in
solving the given problem?
 What is/are the unknown in the given
problem?

17. Lesson No. 5 |Reference Angle
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Explain
Guide Questions:
-What method(s) did you use in solving the
given problem?
-How did you solve the given problem using
that method(s)?
What particular mathematical concept in
trigonometry did you apply to solve the
problem-based task?

18. Lesson No. 5 |Reference Angle
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ELABORATE

19. Lesson No. 5 |Reference Angle
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Elaborate
Generalization of the Lesson:
-How do we find the exact values of
circular functions using reference
angle?

20. Lesson No. 5 |Reference Angle
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Elaborate
Integration of PhilosophicalViews
- In this part, the teacher and learners will relate
the terms/content/process learned in the lesson
about reference angle in real life
situations/scenario/instances considering the
philosophical views that can be
integrated/associated to the
term(s)/content/process/skills of the lesson.

21. Lesson No. 5 |Reference Angle
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Elaborate
Integration of PhilosophicalViews
Questions :
 What are the things/situations/instances that you can
relate with regard to the lesson about reference angle in
real-life?
 Considering your philosophical views, how will you relate
the terms/content/process of the lesson in real-life
situations/instances/scenario?

22. Lesson No. 5 |Reference Angle
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Elaborate
Sample Philosophical Views Integration from the Teacher:
Reference Angle
References Angles are significant in finding the exact
values of circular
functions. Without the reference angle, it is not possible to
find the exact values of the circular function.
In life, our reference angle is the law. We have the Law of
God, the Law of Man, and the Law of Nature.

23. Lesson No. 5 |Reference Angle
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Reference Angle
By looking into these laws, we can tell if an act is an
abomination to God or not; whether we sinned or not. In a
similar manner, the law of man tells us if the person
committed a crime and is guilty beyond a reasonable
doubt. The law of nature tells us to do good and be good
because it is our nature, and it is innate to us because we
are created in the likeness and image of God.

24. Lesson No. 5 |Reference Angle
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Reference Angle
These laws serve as the controlling forces of our
action, our reference angle. Without these laws, we
would not exactly be able to do what is right and
avoid what is wrong. In short, we would fail to find
the exact values of the circular function of knowing
what is good or bad if we don't have this reference
angle.

25. Lesson No. 5 |Reference Angle
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Elaborate
Sample PhilosophicalViews Integration from theTeacher:
Reference Angle
The exact values of the circular function rely on
reference angles. In life, we do what is right and
avoid what is wrong because we are guided by our
reference angle to follow the law. Without these,
we would not be able to find the exact meaning
(value) of ourselves to anyone.

26. Lesson No. 5 |Reference Angle
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EVALUATE

27. Lesson No. 5 |Reference Angle
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Evaluate
Solve the following problems:
a. If P(θ) is a point on the unit circle and θ =
17𝜋
3
,
what are the coordinates of P(θ)?
b. The terminal side of an angle θ in standard
position contains the point (7, –1).
Find the values of the six trigonometric functions
of θ.

28. Lesson No. 5 |Reference Angle
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Evaluate
Solve the following problems:
c. A soccer player x feet from the goalie kicks the ball
toward the goal, as shown in the figure below.The
goalie jumps up and catches the ball 7 feet in the air.
i). Find the reference angle.Then write a
trigonometric function that can be used to find how far
from the goalie the soccer player was when he kicked
the ball.

29. Lesson No. 5 |Reference Angle
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Evaluate
Solve the following problems:
ii). About how far away from the goalie was the
soccer player?

30. Lesson No. 5 |Reference Angle
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Assignment:
Answer the following questions:
1.What is the difference between sine and cosine
graphs?
2. How do we graph sine and cosine functions?
3.What are the domain, range amplitude & period
of sine & cosine functions?
Reference: DepED Pre-Calculus Learner’s Material pages 144-154
-GNDMJR-