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. 2
ANGLES IN STANDARD
POSITION AND
COTERMINAL ANGLES

2. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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ENGAGE

3. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Engagement Activity 1
Angles in Standard Position
Author:Tim Brzezinski
Reference: https://cdn.geogebra.org/resource/wrPcCFNY/rXUcZyPH2PdvsKA2/material-
wrPcCFNY.ggb
• The angle drawn in the coordinate plane is classified as
being drawn in standard position.

4. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Engagement Activity 1
Questions:
1.What can you say about the initial ray and terminal ray
of the given angle?Where does it lie?
2.Where does the vertex of the given angle located?
3.What does it mean for an angle drawn in the
coordinate plane to be in standard position?
4. How do we determine if the given angle drawn is in
standard position?

5. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Small-Group Interactive Discussion
Angle in Standard Position

6. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Small-Group Interactive Discussion
on Angle in Standard Position
Sample inquiry question from the teacher or
learners that will be considered during the small-
group interactive discussion:
-When do we say that an angle is drawn in standard
position?

7. Engagement Activity 2
Coterminal Angles Action!!!
Author:Tim Brzezinski
Reference: https://www.geogebra.org/m/SqQxZqTQ
The given applet dynamically illustrates what it
means for any 2 angles (drawn in standard position)
to be classified as coterminal angles. Learners will
eventually see the formation of one positive angle
and one negative angle that are both coterminal
with each other.
Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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8. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Engagement Activity 2
Questions:
1. Without looking up the definition in the Learner’s
Material (LM), describe, in own words, what it means for
any two angles (drawn in standard position) to be classified
as coterminal angles?

9. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Engagement Activity 2
Questions:
2. a) Is it possible for two positive angles drawn in standard
position to be coterminal?
b) If so, can you give some measures of any two positive
angles that are coterminal?
3. a) Is it possible for two negative angles drawn in standard
position to be coterminal?
b) If so, can you give some measures of any two negative
angles that are coterminal?

10. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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EXPLORE

11. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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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.

12. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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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

13. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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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

14. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Explore
FCA
(Finding Coterminal Angles
Coterminal angles: are angles in standard
position (angles with the initial side on the
positive x-axis) that have a common terminal
side.

15. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Explore
Observe the given illustration on coterminal
angles.

16. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Explore
Problem:
If θ is any angle and for all nonzero integer n, find a
general expression or formula that is coterminal
angle with θ.
Find the angle coterminal with -380° that has
measure between 0° and 360°.
between -360° and 0°.

17. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Explore
FCA
(Finding Coterminal Angles)
Inquiry-Based Guide Questions:
1. What is the multiplier to n in the general
expression or formula?
2. What operation is considered in the general
expression or formula?

18. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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EXPLAIN

19. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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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:

20. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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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 find a general expression or
formula that is coterminal angle with θ?
• How did you convert degree measure to radian measure?
• How did you find the angle coterminal with -380°?

21. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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ELABORATE

22. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Elaborate
Generalization of the Lesson:
• When do we say that a given angle drawn
in xy-plane is in standard position?
• How do we find angle coterminal with the
given angle?

23. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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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 angle in
standard position and coterminal angles 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.

24. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Elaborate
Integration of PhilosophicalViews
Questions :
1.What are the things/situations/instances that you can
relate with regard to the lesson about angle in standard
position and coterminal angles circle in real-life?
2. Considering your philosophical views, how will you relate
the terms/content/process of the lesson in real-life
situations/instances/scenario?

25. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Elaborate
Sample Philosophical Views Integration from the
Teacher:
Coterminal angles can be associated to two or
more persons, organizations, and among others
that have common goal (common terminal side).
The common goal is to find the purpose or meaning
of their existence. One of the purposes is to be a
person or organization for others.

26. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Elaborate
Sample Philosophical Views Integration from the
Teacher:
In finding the purpose and meaning of our
existence, we always consider the people, things or
situations around us. Just like finding an angle (be it
positive or negative) coterminal with the given
angle, a nonzero integer n is always considered to
obtain solution or answer to the given problem.

27. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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EVALUATE

28. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Evaluate
Answer the following:
a. Find a positive angle and negative angle that are
coterminal with the given angle.
i) 60° iv.
𝛱
3
𝑟ad
ii) 120° v. −
𝛱
8
𝑟𝑎𝑑
iii) –90°

29. b) Alex and Alvin are writing an expression for the
measure of an angle coterminal with the angle shown
below. Is either of them correct? Explain your reasoning.
Alex: The measure of a coterminal
angle is (x - 360°)
Alvin: The measure of a coterminal
angle is (360- x°).
Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Evaluate

30. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Assignment:
Answer the following questions:
1.What is an arc length?
2.What is an area of a sector?
3. How do we the relationship between linear and
angular measures of arcs in a unit circle?
Reference: DepED Pre-Calculus Learner’s Material, pages 129-131.

31. Lesson No. 2 | Angles in Standard Position and Coterminal Angles
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Learning Resources:
A. References:
1. Teacher’s Guide pages: 123-135 (DepED SHS Pre-
Calc TG)
2. Learner’s Materials pages: 124-135 (DepED SHS
Pre-Calc LM)
3. Textbook pages: 86-97 (Pre-Calculus Textbook by
J.G. P. Pelias, 1st Ed. 2016)
B. Other Learning Resources: Geogebra Learning
Materials (Applet)
-GENARO NOCETE DE MESA, JR.-