Inquiry-Based Lesson Plans in Pre-Calculus for Senior High School

1
INQUIRY-BASED LESSON PLAN IN PRE-CALCULUS
Lesson Plan No. 1 Time Frame: 1 hour
School: Ocampo National High School Grade Level: 11
Teacher:Genaro N. de Mesa, Jr. Learning Area: Pre-Calculus
Teaching Dates/Time: September 2, 2019/1:00 – 2:00 PM Quarter:2nd
I. OBJECTIVES
A. Content Standard: The learners demonstrate an understanding of key concepts of
circular functions.
B. Performance Standard: The learners are be able to formulate and solve accurately
situational problems involving circular functions.
C. Learning Competencies:
 Convert degree measure to radian measure and vice versa
(STEM_PC11T-IIa-2)
II. CONTENT
3.1: Angles in a Unit Circle
Lesson 3.1.1: Angle Measure
III. 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)
IV. PROCEDURES
Teaching Strategy: Problem-Based Activities using 5 E’s Learning Cycle
Preliminary Activities
1. Greetings
2. Prayer
3. Securing Cleanliness & Orderliness
4. Checking of Assignment
Phase Features
1. Engage
Introduction
- Short video clip entitled “Trigonometry Real Life Application” from
https://www.youtube.com/watch?v=Kd1y5Gobu8I will be played.
- There are situations around us that apply the concept of angles. These include
the fields related to engineering, medical imaging, electronics, astronomy,
geography and many more.
- Surveyors, pilots, landscapers, designers, soldiers, and people in many other
professions heavily use angles and trigonometry to accomplish a variety of
practical tasks.

2
- In this lesson, we will deal with the basics of angle measures.
Engagement Activity
Rotations: Introduction Author: Tim Brzezinski
Topic: Angles, Rotation Reference: https://www.geogebra.org/m/maU9knHU
The applet was designed to help learners better understand what it means
to rotate a point about another point. In the applet, it is free to change the
locations of point A and point B.
Inquiry-Based Questions:
1. Regardless of the amount of rotation, how does the distance AC
compare to the distance AB?
2. Notice how, in the applet, the angle of rotation could be positive or
negative. From what you've observed, what does it mean for a rotation to
have positive orientation (positive angles)? How about for a rotation to
have negative orientation (negative angles)?
-Small-group interactive discussion using Learning Guide Card (LGC) on
Angle Measure will be given to each group.
-The teacher will facilitate the small group interactive discussion.
Inquiry questions from the teacher and learners that will be considered
during the small-group interactive discussion:
-What does the term “angle” mean in Trigonometry?
-How does angle is formed?
-When do we consider angle to be negative in terms of the rotation?
-When do we consider angle to be positive in terms of the rotation?
LGC # 1

3
θ
LGC # 2
To measure angles, we use degrees, minutes, seconds, and radians.
For example, in degrees, minutes, and seconds,
10°30’18” = 10(30+(18/60))
= 10°30.3’
= (10+(30.3/60) °
= 10.505 °
and
79.251 ° = 79 ° (0.251 x 60)’
= 79 °15.06’
= 79 ° 15’(0.06 x 60)”
= 79 ° 15’3.6”.
Recall that the unit circle is the circle with center at the origin and radius 1 unit. A
central angle of the unit circle that intercepts an arc of the circle with length 1 unit is
said to have a measure of one radian, written 1 rad.
1 radian
͌ 57.3 degrees
2. 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.
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
Assigned Role:
Leader – 1 student Peacekeeper/Speaker – 1 student
Secretary/Recorder – 1 student Time Keeper – 1
Material Manager – 1-2 students
Problem-
Based
Activity

4
OMC
(Obtain My Conversion)
Since a unit circle has circumference 2π,a centralangle that measures 360
degrees has measure equivalent to 2π radians.
Problem:
1. Obtain the conversion rules of degree to radian, and vice-versa.
2. What is the radian measure of the following?
a. 90° b. 180° c. –270°
3. What is the degree measure of the following?
a.
Π
4
rad b.
2Π
3
rad c. −
𝛱
3
𝑟𝑎𝑑
Inquiry-Based Guide Questions:
1. What is your multiplier in converting a degree measure to radian
measure?
2. What is your multiplier in converting a radian measure to degree
measure?
3. Explain
- Group Leader/Representative will present the solutions and answer to the class
by explaining the problem/concept explored considering the following 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?
 How did you convert degree measure to radian measure?
 How did you convert radian measure to degree measure?
4. Elaborate
- Brief discussion of some examples about Converting Degree Measure to
Radian Measure,and vice versa
Generalization of the Lesson:
-What are the steps in converting angles from degree to radian, and vice versa?
Integration of Philosophical Views:
- In this part, the teacher and learners will relate the terms/content/process
learned in the lesson about angle measure 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.
- Questions to be asked:
 What are the things/situations/instances that you can relate with regard to
the lesson about angle measure in real-life?
 Considering your philosophical views, how will you relate the
terms/content/process of the lesson in real-life
situations/instances/scenario?

5
- Philosophical Views Integration from the Teacher:
Angle measure includes angles classified as acute, obtuse, right, positive
angle, and negative angles. People look into things, events, and situations in
different angles. True wisdom is looking at things from a wide (obtuse) and
positive angle. This way, we would be able to examine the situations, look for
fresh dots, explore the things we thought we knew, and trigger new insights.
On the other hand, if we look at our troubles, difficulties, and problems in a
narrow or acute and in a clockwise direction or negative angle, we may not find
any solution to the problem we are currently facing. Many operational approaches
center too narrowly on problem management to reduce the variation rather than
create a space to think and allow new ways of looking at the situation as a whole,
the doorstep to the breakthrough creativity. Thus, if we look from a wide-angled
view and in a counter-clockwise direction or positive angle, we can see that they
are tiny and trivial in relation to the whole world. It makes it easier for us to be
strong and to deal healthily and positively with these troubles, difficulties, and
problems.
Integration of
Philosophical
Views
5. Evaluate
Answer the following:
a. Convert each degree measure to radians. Leave answers in terms of 𝜋.
i) 150° ii) 330° iii) –480°
b. Convert the following radian measures to degree measure.
i)
𝛱
6
𝑟𝑎𝑑 ii)
Π
10
rad iii) −
3Π
5
rad
V. ASSIGNMENT
Answer the following questions:
1. How do we illustrate angles in standard position?
2. How do we illustrate coterminal angles?
Reference: DepEDPre-Calculus Learner’s Material,pages125-129.

6
Lesson Plan No. 2 Time Frame: 1 hour
I. OBJECTIVES
circular functions.
 Illustrate angles in standard position and coterminal angles
(STEM_PC11T-IIa-3)
II. CONTENT
Lesson 3.1.2: Angles in Standard Position and Coterminal Angles
A. References:
Ed. 2016)
IV. PROCEDURES
1. Greetings
2. Prayer
5. Review of Previous Lesson
Phase Features
1. Engage
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.

7
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?
Small-group interactive discussion using Learning Guide Card
(LGC) on Angle in Standard Position will be given to each group
Learning Guide Card (LGC)
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?
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.
An angle is in standard position if it
is drawn in the xy-plane with its
vertex at the origin and its initial side
on the positive x-axis.
The angles ɑ, β, and θ in the given
figure are angles in standard
position.

8
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?
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?
2. Explore
Assigned Role:
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.
Observe the given illustration on coterminal angles.
Problem-
Based
Activity

9
Problem:
1. If θ is any angle and for all nonzero integer n, find a general expression
or formula that is coterminal angle with θ.
2. Find the angle coterminal with -380° that has measure
a) between 0° and 360°.
b) between -360° and 0°.
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?
3. Explain
 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°?
4. Elaborate
- Brief discussion of some examples about finding coterminal angles
- 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?
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.

10
 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?
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.
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.
Integration of
Philosophical
Views
5. Evaluate
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°
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°).
V. ASSIGNMENT
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?

11
Lesson Plan No. 3 Time Frame: 2 hours
I. OBJECTIVES
circular functions.
 Illustrate the unit circle and the relationship between the linear and
angular measures of a central angle in a unit circle.
(STEM_PC11T-IIa-1)
II. CONTENT
Lesson 3.1.3: Arc Length and Area of a Sector
A. References:
Ed. 2016)
IV. PROCEDURES
1. Greetings
2. Prayer
5. Review of Previous Lesson
Phase Features
1. Engage
Linear and Angular measures
Author: Irina Boyadzhiev
Reference:https://www.geogebra.org/m/EazPPkFV

12
The applet illustrates the linear and angular measures of central angle in
a unit circle.
Questions:
:
2. What can you say about the linear measure of angle? How about angular
measure?
3. Is there a relationship between angular and linear measures of angle?
4. What can you infer about the relationship of angular and linear measures
of angle?
Learning Guide Card (LGC) # 1
Arc Length
The length of an arc on a circle of radius r is equal to the radius
multiplied by the angle θ subtended by the arc in radians. Using s to denote arc
length we have s = rθ.
This should actually be intuitive since the arc length on the unit circle is
equivalent to the angle in radians.
The figure below shows arc length between Points A and B on the circle.
Since we are looking at a length, we always consider the angle θ subtended by A
and B to be positive. (In each of the next two figures, both and can be moved.)
Inquiry Guide Questions (IGQ) for Interactive Arc Length using Geogebra

13
applet:
-What can you say about the length of an arc on a circle?
-How is the arc length on the unit circle related to the angle in radians?
Learning Guide Card (LGC) # 1
Area of a Circular Sector
Recall that the area of a circle of radius is given by A = π𝑟2
.
A circular sector is a wedge made of a portion of a circle based on the central
angle θ (in radians) subtended by an arc on the circle. Since the angle around the
entire circle is 2π radians, we can divide the angle of the sector's central angle by
the angle of the whole circle 2π to determine the fraction of the circle we are
solving for. Then multiply by the area of the whole circle to derive the sector
area formula.
Inquiry Guide Questions (IGQ) for Interactive Area of Circular Sector using
Geogebra applet:
- What can you say about the area of a circular sector?
- How do we determine the fraction of the circle we are solving in area of
circular sector?
2. Explore
Assigned Role:
Problem 1 (Group 1 & Group 2): Minute Hand of a Clock
The minute hand of a clock is 6 inches long. (a) How far does the tip of the
Problem-
Based
Activity

14
minute hand move in 15 minutes? (b) How far does it move in 25 minutes?
Problem 2 (Group 3 & Group 4): Movement of a Pendulum
A pendulum swings through an angle of 20° each second. If the pendulum is 40
inches long, how far does its tip move each second?
Problem 3 (Group 5 & Group 6): Linear Speed v. Angular speed
Our earlier “obvious” equation s = rθ, relating arc to angle, also works with
measurements of speed. The angular speed of an spinning object is measured in
radians per unit of time. The linear speed is the speed a particle on the spinning
circle, measure in linear units (feet,meters) per unit of time.
Suppose a merry-go-round is spinning at 6 revolutions per minute. The radius of
the merry-go-round is 30 feet. How fast is someone traveling if they are standing
at the edge of the merry-go-round?
Problem 4 (Group 7 & Group 8): Watering a Lawn
A water sprinkler sprays water over a distance of 30 feet while rotating through
an angle of 135°. What area of lawn receives water?
3. Explain
 What is/are the unknown in the given problem?
 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?
4. Elaborate
- Brief discussion of some examples about solving problems involving arc length
and area of circular sector.
- What is the relationship between linear and angular measure of arcs?
- What are the steps in solving problems on arc length and area of a sector?
learned in the lesson about arc length and area of a sector in real life
 What are the things/situations/instances that you can relate with regard
to the lesson about arc length and area of a sector in real-life?

15
V. ASSIGNMENT
1. What are the six trigonometric functions?
2. What is a reference angle?
Circle and radius are one of the terms used in this lesson has many real-life
connections. A circle is a line forming a closed-loop; every point on which is a
fixed distance from a center point. Imagine a straight line segment bent around
until its ends join, then arrange that loop until it is exactly circular - that is, all
points along that line are the same distance from a center point. Unlike other
shapes, a circle has a unique property of being complete. A circle has an
extensive meaning; it represents wholeness, totality, original perfection, eternity,
infinity, timelessness, self, and all the cyclic movement. According to Hermes
Trismegistus, God is a circle whose center is everywhere and whose
circumference is nowhere. Circle implies the idea of a movement and symbolizes
the cycle of time - the perpetual motion of everything that moves like the planet's
journey around the sun and the rhythm of the universe. Many people believe that
if they have God in them, they are complete, and people who feel complete are
stronger and happier.
The distance from the center to any point of the circle is known as the
radius. Each unit or radius of the circle helps the circle to resist giving into forces
putting pressure on it from the outside. Similarly, each of this unit is a person's
faith. Plenty of this strengthens the grip so as not to be swayed by the evil.
Life is a circle because of the same and continues progression from birth and
growth to decline and death.
Integration of
Philosophical
Views
5. Evaluate
Solve the following problems:
a. The minute hand of a clock is 5 inches long. How far does the tip of the
minute hand move in 30 minutes?
b. An automatic lawn sprinkler sprays up to a distance of 20 feet while rotating
30 degrees. What is the area of the sector the sprinkler covers?
c. Find the area of a sector of a circle with centralangle of
7𝜋
6
if the diameter of a
circle is 9 cm?
d. A swing has 165° angle of rotation.
i) If the chains of the swing are 6 feet long, what is the length of the arc that
the swing makes? Round your answer to the nearest tenth.
ii) Describe how the arc length would change if the length of the chains of the
swing were doubled.

16
I. OBJECTIVES
circular functions.
 Illustrate the different circular functions
(STEM_PC11T-IIb-1)
II. CONTENT
3.2: Circular Function
Lesson 3.2.1: Circular Functions on Real Numbers
A. References:
2. Learner’s Materials Pages:135-144 (DepED SHS Pre-Calc LM)
3. Textbook pages:
IV. PROCEDURES
1. Greetings
2. Prayer
Phase Features
1. Engage
Introduction
-A Trigo function song in the tune of “One Call Away” downloaded from
youtube https://www.youtube.com/watch?v=_M6WdLP2Qqo will be played.
-We define the six trigonometric function in such a way that the domain of each
function is the set of angles in standard position. The angles are measured either
in degrees or radians.
-In this lesson, we will modify these trigonometric functions so that the domain

17
will be real numbers rather than set of angles.
“Unit Circle - Exact Values”
Task: Investigate the exact trigonometric values using Geogebra applet by
dragging the green dot around the unit circle.
Author: Nick Kochis Topic:Circle, Unit Circle
Reference:https://www.geogebra.org/m/G7xgNRxm
Questions:
1. Do you observe any patterns with the sine and cosine functions relating
to the coordinates?
2. How will you relate the coordinates with the sine and cosine functions?
- Small-group interactive discussion using Learning Guide Card (LGC) on
Circular Functions on RealNumbers will be given to each group.
(Note: Short review on Pythagorean Theorem and Properties of Special Right
Triangles will be given before the small-group interactive discussion)
- The teacher will facilitate the small group interactive discussion.
Inquiry questions that will be considered during the activity:
- What are the values of the circular functions on real numbers
considering θ as the given angle and P(θ) = P(x, y) be the point on
the unit circle?
- How do we define the six functions on real numbers if we let s be
any real number and θ be the angle in standard position with measure
s rad?
- How do we find the exact values of trigonometric functions
considering the coordinates of the terminal point on the unit circle of
the given angle?
- How do we define the six circular functions if θ be an angle in
standard position, Q(x, y) any point on the terminal side of θ, and
r = √𝑥2 + 𝑦2 > 0?

18
Let θ be an angle in standard position and let P(θ) = P(x, y) the
point on its terminal side on the unit circle. Define
sin θ = y csc θ =
1
𝑦
, y ≠ 0
cos θ = x sec θ =
1
𝑥
, x ≠ 0
tan θ =
𝑦
𝑥
, x ≠ 0 cot θ =
𝑥
𝑦
, y ≠ 0
Let s be any real number. Suppose θ is the angle in standard
position with measure s rad. Then we define
sin s = sin θ csc s = csc θ
cos s = cos θ sec s = sec θ
tan s = tan θ cot s = cot θ
Let θ be an angle in standard position, Q(x, y) any point on the
terminal side of θ, and r = √𝑥2 + 𝑦2 > 0. Then
sin θ =
𝑦
𝑟
csc θ =
𝑟
𝑦
, y ≠ 0
cos θ =
𝑥
𝑟
sec θ =
𝑟
𝑥
, x ≠ 0
tan θ =
𝑦
𝑟
, x ≠
2. Explore
Assigned Role:
Problem-
Based
Activity

19
Problem 1 (Group 1 & Group 2):
Find the values of cos 135°, tan 135°, sin(-60°), and sec (-60°).
Problem 2 (Group 3 & Group4):
Find the exact values of sin
3𝜋
2
, cos
3𝜋
2
, and tan
3𝜋
2
.
Suppose s is a realnumber such that sin s = −
3
4
and cos s > 0. Find cos s.
Suppose s is a realnumber such that cos s =
1
2
and sin s > 0. Find sin s.
3. Explain
4. Elaborate
- Brief discussion of some examples about solving problems involving circular
functions on realnumbers
- Considering θ as the given angle and P(θ) = P(x, y) be the point on the
unit circle, what are the values of the six circular functions on real
numbers?
-
learned in the lesson about circular functions on real numbers in real life
to the lesson about circular functions on real numbers in real-life?

20
V. ASSIGNMENT
2. How do we find the value of a circular function at a number θ?
Circular Functions on Real Numbers deal with finding the exact values of a
given angle. In real-life, the exact values of a given angle can be connected or
associated to our value or worth in dealing life’s function as a person to others. In
finding our worth or value, there are things (angles) that must be considered.
These are the people, things, situations that contributed in the attainment of one’s
worth. Without these, we would not be able to find the exact meaning (value) of
ourselves to anyone.
Integration of
Philosophical
Views
5. Evaluate
a. Find the values of:
i) sin 30° ii) cos 150° iii) tan (-150°) iv) sec (-30°)
b. Find the exact values of:
i) sin
11𝜋
6
ii) cos
11𝜋
` 6
iii) tan
11𝜋
6
iv) cot (−
4𝜋
3
)
c. Determine whether 3 sin 60° = sin 180° is true or false. Explain your answer.

21
I. OBJECTIVES
circular functions.
 Use reference angles to find exact values of circular functions
(STEM_PC11T-IIb-2)
II. CONTENT
3.2: Circular Function
Lesson 3.2.2: Reference Angle
A. References:
2. Learner’s Materials Pages:135-144 (DepED SHS Pre-Calc LM)
3. Textbook pages:
IV. PROCEDURES
1. Greetings
2. Prayer
Phase Features
1. Engage
Engagement Activity
Investigating Reference Angle
Author: Scott Farrar
Topic: Angles, Triangles
Reference:http://www.geogebra.org

22
Drag P.
Questions:
2. What is the use of a reference angle?
3. How do we find a reference angle?
-Small-group interactive discussion using Learning Guide Card (LGC) on
Reference Angle.
(The teacher will facilitate the small group interactive discussion.)
Inquiry questions from the teacher and learners that will be considered during the
activity:
- 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?
- How do we determine the value of a particular circular function at an angle
θconsidering the correct sign? How do we determine the correct sign?
- Where does the sign of the coordinates of P(θ) depends?

23
2. Explore
Assigned Role:
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-
Based
Activity
the figure.

24
Find the exact value of each expression using reference angle & appropriate sign.
a) cos (−
11𝜋
6
) b) tan
8𝜋
3
and cot
8𝜋
3
Find the six trigonometric functions of the angle θ if the terminal side of θ in
standard position passes through (5, -12)
If P(θ) is a point on the unit circle and θ =
5𝜋
6
, find the values of the six
trigonometric functions of θ.
3. Explain
4. Elaborate
- Brief discussion of some examples about problems on finding the exact values
of circular functions using reference angle.
- How do we find the exact values of circular functions using reference
angle?
learned in the lesson about reference angle in real life
to the lesson about reference angle in real-life?
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. By looking into these laws, we can tell if an act is
Integration of
Philosophical
Views

25
V. ASSIGNMENT
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
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. 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. 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.
5. Evaluate
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.
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.
ii). About how far away from the goalie was the soccer player?

26
I. OBJECTIVES
A. Content Standards: The learners demonstrate an understanding of key concepts of
circular functions.
B. Performance Standards: The learners are able to formulate and solve accurately
 Determine the domain and range of the different circular functions
(STEM_PC11T-IIc-1)
 Graph the six circular functions (a) amplitude, (b) period and (c) phase shift
(STEM_PC11T-IIc-d-1)
II. CONTENT
3.3: Graphs of Circular Functions and Situational Problems
3.3.1: Graphs of y = sin x and y = cos x
3.3.2: Graphs of y = a sin bx and y = a cos bx
3.3.3: Graphs of y = a sin b(x – c) + d and y = a cos b(x – c) + d
A. References:
2. Learner’s Materials Pages: 144-170 (DepED SHS Pre-Calc LM)
3. Textbook pages:
B. Other Learning Resources: Geogebra Learning Materials (Applet)
IV. PROCEDURES
1. Greetings
2. Prayer
Phase Features
1. Engage
- Introduction
There are many things that occur periodically. Phenomena like rotation of the
planets and comets, high and low tides, and yearly change of the seasons follow a

27
periodic pattern. In this lesson, we will graph circular functions and we will see
that they are periodic in nature.
“Domain & Range Illustrator” – Review on domain and range of a function
Author :Tim Brzezinski Topic: Functions
Reference:https://www.geogebra.org/m/DUx2uB5f
Questions:
1. What can you say about the domain of the given function?
2. What can you say about the domain of the given function?
3. How will you define (in your own words) the domain of any function?
4. How will you define (in your own words) the range of any function?
The Graph of Sine & Cosine Functions Author:Tim Brzezinski
Topic: Cosine, Functions, Function Graph, Sine, Trigonometric Functions
The learners will interact with the given Geogebra applet. Then they will answer
the questions that follow.

28
Questions:
1) Consider the function f(x) = sin(x).
What are the values of a, b, c, and d for this parent sine function? What is its
period? How about amplitude?
2) What do the parameters a, b, c, and d do to the graph of the function f(x) =
sin(x) under the transformation y = a*sin(bx - c) + d?
3) Consider the function g(x) = cos(x).
What are the values of a, b, c, and d for this parent cosine function? What is its
period? How about amplitude?
4) What do the parameters a, b, c, and d do to the graph of the function f(x) =
cos(x) under the transformation y = a*cos(bx - c) + d?
5) What are the domain and range of f(x) = sin(x)? How about g(x) = cos(x)?
The Graph of Sine & Cosine Functions
- Small-group interactive discussion using Learning Guide Card
(LGC) on Graphs of Sine & Cosine Functions will be given.
Inquiry guide questions that will be considered during the activity:
- What can you say about the graphs of sine and cosine functions in
terms of the following:
Domain, Amplitude, Range, and Period?
- What are the domains of the sine and cosine functions?
- What are the ranges of the sine and cosine functions?
- What are the periods of the sine and cosine functions? What does
period mean?
- How does the amplitude affect the graph of the sine or cosine
functions?
- How do you graph sine and cosine functions? What are the things to
be considered in graphing the said functions?
- What are the important properties of the graphs of sine and cosine
functions?

30
2. Explore
Assigned Role:
Problem-
Based
Activity

31
Sketch the graph of one cycle of y = 3 sin (x +
𝛱
4
) and y = 3 cos (x +
𝛱
4
)
with its amplitude, period and phase shift. Determine the domain and range of the
function.
Sketch the graph of one cycle of y =
1
2
sin (−
2𝑥
3
) and y =
1
2
cos (−
2𝑥
3
) with
its amplitude, period and phase shift. Determine the domain and range of the
function.
Sketch the graph of one cycle of y = −3𝑠𝑖𝑛
𝑥
2
and y = −3𝑐𝑜𝑠
𝑥
2
with
its amplitude, period and phase shift. Determine the domain and range of
the function.
Sketch the graph of one cycle of y = 2 sin 4𝑥 and y = 2 cos4𝑥 with its
amplitude, period and phase shift. Determine the domain and range of the
function.
3. Explain
4. Elaborate
- Brief discussion of some examples of graphing sine and cosine functions
- What are the properties of the graphs of sine and cosine functions?
- What are the domain and range of sine and cosine Functions?
- How do we determine the Amplitude, Period, and Phase Shift of Sine and
Cosine Functions?
Integration ofPhilosophical Views:
- In this part, the teacher and the learners will relate the terms/content/process
learned in the lesson about Graphs of Sine and Cosine Functions in real life
integrated/associated to term(s)/content/process/skills of the lesson.
 What are the things/situations/instances that you can relate with regards to the
lesson about Graphs of Sine and Cosine Functions?

32
V. ASSIGNMENT
. Answer the following questions:
1. What is the difference between secant and cosecant graphs?
2. How do we graph secant and cosecant functions?
3. What are the domain, range & period of sine & cosine functions?
Reference: DepEDPre-Calculus Learner’s Material,pages154 – 157
 How will you connect the terms/content/process of the lesson in real-life
situations/instances/scenario considering your philosophical views?
Philosophical Views Integration from the Teacher:
The graphs of sine and cosine can be found everywhere. It is present
in the radio waves, electrical currents, tides, and musical tones. When we
look at seismic waves on a map of what is happening beneath us, we can
see this graph. The graphs of the sine and cosine both have the hills and
valleys in a repeating pattern. In life, this pattern signifies the ups and
downs that people face. We see the sine curves the way we react on things
naturally like the occurring phenomena. Take water waves as an example;
when waves have more energy, the more vigorous they go up and down.
The amplitude - the distance from the resting position is an indication of
the amount of energy that the waves contain.
In the same manner, when people have low amplitude, they have
low energy to fight against the challenges that they are facing. With them
becoming less energetic, the less vigorous the graphs go up or down. The
graph of the sine at the beginning shows the people when they are at the
top while the beginning of the cosine shows the bottom. The movement
depends on the energy of the person. The graph may go down or may rise.
Integration of
Philosophical
Views
5. Evaluate
a) Sketch the graph of the function y = −2 cos (x −
𝛱
2
) + 3 over two periods.
b) Graph the given sine and cosine functions with its amplitude, period, and phase
shift and determine its domain & range.
i) y = 3sin(x)and y = 3cos(x)
ii) y = −sin(x +
𝜋
3
) and y = −cos(x +
𝜋
3
)
c) Explain how to find the amplitude of y = −3sinx and describe how the
negative coefficient affects the graph.
d) How will you compare and contrast the graphs of y = 2sinx and y = sin 2x?

33
I. OBJECTIVES
circular functions.
B. Performance Standards: The learners are be able to formulate and solve accurately
(STEM_PC11T-IIc-1)
 Graph the six circular functions (a) amplitude, (b) period, and (c) phase shift
II. CONTENT
3.3.4: Graphs of Cosecant and Secant Functions
A. References:
3. Textbook pages:
IV. PROCEDURES
1. Greetings
2. Prayer
Phase Features
1. Engage
Interactive activity using Geogebra Applet on Graph of Cosecant and
Secant Functions

34
Illustrating Cosecant with the Unit Circle
Author:afrewin Reference:https://www.geogebra.org/m/xcVNZQ9G
Topic:Trigonometry
The applet allows us to explore the relationship between the unit circle and the
cosecant function.
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?
The Graph of Cosecant & Secant Functions
-Small-group interactive discussion using Learning Guide Card (LGC) on Graphs
of Cosecant & Secant Functions will be given.

35
-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?
-Do cosecant and secant functions have amplitude? Why?
-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?
- What are the important properties of the graphs of cosecant and secant
functions?

36
2. Explore
Assigned Role:
Problem-
Based
Activity

37
Sketch the graph of y =
1
2
csc (x +
𝛱
4
) over two periods. Determine its domain
and range.
Sketch the graph of y = 2 – sec 2x over two periods. Determine its domain and
range.
Sketch the graph of y = 2 csc
𝑥
2
over two periods. Determine its domain and
range.
Problem 1 (Group 7 & Group 8)
Sketch the graph of y = 3 sec2x over two periods. Determine its domain and
range.
3. Explain
4. Elaborate
- Brief discussion of some examples about graphing cosecant and secant
functions
- 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?
In this part, the teacher and the learners will relate the
terms/content/process learned in the lesson 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.
Questions to be asked:

38
V. ASSINMENT
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
- What are the things/situations/instances that you can relate with regards to
the lesson about Graphs of Cosecant and Secant Functions?
- How will you relate the terms/content/process of the lesson in real-life
The graph of sine and cosine function is used as a guide in graphing cosecant
and secant functions, respectively. 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.
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 almost a straight
line of your life.
Integration of
Philosophical
Views
5. 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
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)?

39
I. OBJECTIVES
circular functions.
B. Performance Standards: The learners are be able to formulate and solve
accurately situational problems involving circular functions.
(STEM_PC11T-IIc-1)
 Graph the six circular functions (a) amplitude, (b) period, and (c) phase shift
II. CONTENT
3.3.5: Graphs of Tangent and Cotangent Functions
A. References:
3. Textbook pages:
IV. PROCEDURES
1. Greetings
2. Prayer
Phase Features
1. Engage
Interactive activity using Geogebra Applet on Graph of Tangent and
Cotangent Functions
Illustrating Tangent and Cotangent with the Unit Circle

40
Author: afrewin
Topic: Tangent Function, Trigonometry
References:https://www.geogebra.org/m/YUJvBfxw#material/fbQWQGsg
https://www.geogebra.org/m/YUJvBfxw#material/ueUcqGNG
Questions:
1. What can you say about the relationship between the tangent and
cotangent function with the unit circle?
2. How will you describe the relationship between the tangent and
cotangent function with the unit circle?
Tangent Cotangent Relationship
Author:carpenter Reference:https://www.geogebra.org/m/Y74C5aNz
Move the parameters a (vertical dilation), b (period dilation), c ( part of phase
shift), and d (vertical shift) to see how the graphs of tangent and cotangent are
related
Questions:
1. Based on the graph, what can you say about the domain and range of
tangent function? How about cotangent function?
2. How will you describe the relationship of tangent and cotangent function in
terms if their domain, range and phase shift?
The Graph Tangent & Cotangent Functions

41
-Small-group interactive discussion using Learning Guide Card (LGC) on Graphs
of Tangent & Cotangent Functions will be given.
-What can you say about the graphs of tangent and cotangent functions in terms
of the following: Domain; Range; Phase Shift and; Period?
-What is your guide in graphing tangent and cotangent functions?
-What are the important properties of the graphs of tangent and cotangent
functions?
-Do tangent and cotangent functions have amplitude? Why?
-What are the domains of the tangent and cotangent functions?
-What are the ranges of the tangent and cotangent functions?
-What are the periods of the tangent and cotangent? What does period mean?
How do you find the period of a given tangent or cotangent functions?
-How do you graph tangent and cotangent functions? What are the things to be
considered in graphing the said functions?

42
2. Explore
Assigned Role:
Sketch the graph of y = 1/2 tan 2x over three periods. Find the domain and
range of the function.
Sketch the graph of y = 2 cot 1/2 x over three periods. Find the domain and
Problem-
Based
Activity

43
Sketch the graph of y = –tanx + 2 over three periods. Find the domain and
Sketch the graph of y = –2cotx – 1 over three periods. Find the domain and
3. Explain
4. Elaborate
- Brief discussion of some examples about graphing tangent and cotangent
functions
Generalization ofthe Lesson:
- What are the properties of the graphs of tangent and cotangent functions?
- What are the domain and range of tangent and cotangent functions?
- How do we determine the asymptotes, period and phase shift of tangent and
cotangent functions?
- In this part, the teacher and the learners will connect the
terms/content/process learned in the lesson about Graphs of Tangent
and Cotangent 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.
 What are the things/situations/instances that you can relate
with regards to the lesson about Graphs of Tangent and
Cotangent Functions?
 How will you connect the terms/content/process of the lesson
in real-life situations/instances/scenario considering your
philosophical views?
The graph of tangent and cotangent functions extends to positive and
negative infinity. There are specific points where the graph is undefined and
where the graph is restricted. As the concepts and properties of tangent and
Integration of
Philosophical
Views

44
V. ASSINMENT
1. What is meant by simple harmonic motion?
2. What are the equations of simple harmonic motion?
3. Give example of solved situational problems involving graphs of
circular functions.
Reference: DepEDPre-Calculus Learner’s Material,pages160-165
cotangent functions in real life, there are specific instances in our life that our
undertakings have a positive or a negative outcome. There can also be instances
where the result is limited. Based on Newton's third law of motion, for every
action, there is an equal and opposite reaction.
The result of your action may have infinite advantages or endless
disadvantages, but there may be a limited result. In most cases, you consider your
comfort zone, whereas, you restrict yourself from learning and experiencing new
things because you do not want to take the risk. You want a situation in which
you feel comfortable by not testing your ability and determination. Your comfort
zone is your behavioral space where your activities and behaviors fit the routine
and pattern that minimizes stress and risk. There is a sense of familiarity,
security, and certainty in your comfort zone. So, opening yourselves up to the
possibility of stress and anxiety when you step outside of your comfort zone is a
difficult thing for you to do. However, you would never know what life has to
bring to you if you would try. Remember that it is good to step out, and to
challenge yourself to perform to the best of your ability. You never know the kind
of life that you may have been. It can be like the graph of tangent and cotangent
function that extends to positive infinity, instead of staying at the negative
infinity.
5. Evaluate:
a) Sketch the graph of the function y =
1
4
tan (𝑥 −
𝛱
4
) over three periods. Find the
domain and range of the function.
b) Graph the given tangent and cotangent functions with its period, and phase
shift and determine its domain & range.
i) y =
1
2
cot(
1
3
𝑥) + 2 ii) y = −4 tan(𝑥 −
𝛱
4
) − 1
c) How does the graph of y =
1
2
tan x + 1 is different from y = tan x?
d) Are the graphs of y = 𝑐𝑜𝑡 (x) − 1 different from the graph of y = cot (x)?
Justify your answer.

45
Teaching Dates/Time: September 25-26 & October 1, 2019/1:00 – 3:00 PM
Quarter:2nd
I. OBJECTIVES
circular functions.
B. Performance Standards: The learners are be able to formulate and solve accurately
 Solve problems involving circular functions
(STEM_PC11T-IId-2)
II. CONTENT
.3.6: Simple Harmonic Motion
A. References:
3. Textbook pages:
B. Other Learning Resources
IV. PROCEDURES
Teaching Strategies: Problem-Based, Project-Based and Design-BasedActivities
using 5 E’s Learning Cycle
Session1
1. Greetings
2. Prayer
Phase Features
1. Engage
Introduction
Repetitive or periodic behavior is common in nature. As an example, the time-

46
telling device known as sundial is a result of the predictable rising and setting of
the sun everyday. It consists of a flat plate and a gnomon. As the sun moves
across the sky, the gnomon casts a shadow on the plate, which is calibrated to tell
the time of the day.
- Interactive Simple Harmonic Motion illustrations using Geogebra Applet will be
utilized.
Questions:
1. What can you say about the interactive simple harmonic motion?
2. What happens to the weight when it is suspended on a spring, pulled
down and released?
3. Neglecting resistance,what will happen to the oscillatory motion of the
weight?
4. Is the height of the oscillatory motion periodic with respect to time?
Why do you say so?
Simple Harmonic Motion - Ferris Wheel
Author: jeromeawhite
Topic: Trigonometry
Simple Harmonic Motion as displayed through the motion of a Ferris
wheel
Reference:https://www.geogebra.org/m/XhKqBhvx#material/qyfesjMV
Simple Harmonic Motion – Pendulum

47
Author: jeromeawhite Topic: Trigonometric Functions Trigonometry
Simple Harmonic Motion as displayed through the swinging of a
pendulum.
Reference: https://www.geogebra.org/m/XhKqBhvx#material/zFfuZWNt
Simple Harmonic Motion – Piston
Author: jeromeawhite Topic: Sine, Trigonometry
Simple Harmonic Motion as displayed through the motion of a piston
Reference:https://www.geogebra.org/m/XhKqBhvx#material/GmnRkHsc
Simple Harmonic Motion - Masson a Spring
Author: jeromeawhite Topic: Function Graph, Trigonometry
Reference:https://www.geogebra.org/m/XhKqBhvx#material/Ne3TwAdW
Simple Harmonic Motion as displayed through the motion of a mass oscillating
from a spring

48
(Inquiry questions from the learners and teacher will be considered after
illustrating the 5 simple harmonic motion as one of the applications of circular
functions,particularly graphs of sine and cosines functions)
Sample Inquiry Questions:
1. What can you say about the interactive simple harmonic motion illustrations
using Geogebra Applet?
2. What does each of the sliders represent in the respective simple harmonic
motion illustrations?
3. How will you describe the graphs considering the horizontal position of the
point at the top as a function of time in the respective simple harmonic motion
illustrations?
4. How does the graphs of circular functions concept, particularly sine and
cosine functions are applied in simple harmonic motion illustrations?
Simple Harmonic Motion
- Small-group interactive discussion using Learning Guide Card (LGC) on
Simple Harmonic Motion will be given.
- Inquiry questions from the teacher and learners will be considered during the
activity.
- What are the examples of real-life occurrences that behave in simple harmonic
motion considering unimpeded movements?
- What are the equations of simple harmonic motions?
- How will you describe the information on equations of simple harmonic
motions?

49
2. Explore
Exploration Activity 1 (Problem-Based Activity)
Problem-
Based
Activity

50
1 point – Correct Answer but No Explanation/Solutions
Assigned Role:
Problem 1 (Group 1 & Group 2): Ferris Wheel
A carnival Ferris wheel with a radius of 14 m makes one complete revoluti
on every16 seconds. The bottom of the wheel is 1.5 m above the ground.
If a person is at the top of the wheel when a stop watch is started,
determine how high above the ground that person will be after 1 minute
and 7 seconds? Sketch one period of this function.
Problem 2 (Group 3 & Group 4): Ocean Tides
The alternating half-daily cycles of the rise and fall of the ocean are called t
ides. Tides in one section of the Bay of Fundy caused the water level to rise
6.5m above mean sea-level and to drop 6.5m below. The tide completes
one cycle every 12 hours.
Assuming the height of water with respect to mean sea-level to be
modelled by a sine function,
(a) draw the graph for a the motion of the tides for one complete day;
(b) find an equation for the graph in (a).
Problem 3 (Group 5 & Group 6): Roller Coaster
John climbs on a roller coaster at Six Flags Amusement Park. An observer
starts a stopwatch and observes that John is at a maximum height of 12 m
at t = 13.2 s. At t = 14.6 s, John reaches a minimum height of 4 m.
a) Sketch a graph of the function.
b) Find an equation that expresses John's height in terms of time.
c) How high is John above the ground at t = 20.8 s?

51
Problem 4 (Group 7 & Group 8): Spring Problem
A weight attached to a long spring is being bounced up and down by an
electric motor.
As it bounces, its distance from the floor varies periodically with time.
You start a stopwatch,when the stopwatch reads 0.3 seconds, the weight
reaches its first high point 60 cm above the ground. The next low point, 40
cm above the ground, occurs at 1.9 seconds.
a) Sketch a graph of the function.
b) Write an equation expressing the distance above the ground in terms of
the numbers of seconds the stopwatch reads.
c) How high is the mass above the ground after 17.2 seconds?
Sessions 2 and 3
1. Greetings
2. Prayer
5. Recall
Exploration Activity 2 (Project-Based Activity)
a project-based task card to be explored, accomplished and presented to the class.
Inquiry-based questions from the teacher and learners will be considered during
the exploration activity.
0 point – No task explored, accomplished and presented
1 point – Correct Output but No Explanation/Solutions & Presentation
2 points - Correct Output with Explanation/Solutions & Presentation
3 points - Correct Output with well-Explained/with Systematic Solution &
Presentation
(Note: Adapted Project-Based Output Rubric will also be utilized)
Assigned Role:
General Task
Objectives: To formulate, solve and present accurately situational
problems involving circular functions.
Specific Task Objectives:
1. Create two situational problems involving circular functions
particularly simple harmonic motion concept application
2. Prepare interactive powerpoint presentation of the situational problems
created.
Project-
Based
Activity

52
3. Discuss the situational problems created within the group.
4. Present the situational problems created to the class.
Sessions 4 and 5
1. Greetings
2. Prayer
5. Recall
Exploration Activity 3 (Design-Based Activity)
The class will be divided into 8 groups (5-6 members). Each group will be
given a design-based task card to be explored, created and presented to the class.
0 point – No Output Explored, Created and Presented
1 point – Correct/Accurate Output but No Explanation/Solutions
2 points - Correct/Accurate Output with Explanation/Solutions
3 points - Correct/Accurate Output with well-Explained/with Systematic Solution
(Note: Adapted Design-Based Output Rubric will also be utilized)
Assigned Role:
General Task
Objectives:
1. To formulate and graph circular functions model.
2. To design a work of art using the graph of circular functions
Specific Task
Objectives:
1. To create circular functions model.
4. To graph circular functions model.
3. To design/make creative output using the graphs of circular
functions.
4. To present the design-based output to the class.
DBL Goal: Use at least 3 different trigonometric parent function graphs to create
a design-based art output.
Requirements:
1) Art must include a minimum of 3 different trig parent functions
Design-
Based
Activity

53
showing 2 or more periods of each function. At least two of the
functions must include shifts (vertical or horizontal or both).
At least one function must have a period other than 2π.
2) Use one-fourth of large poster board.
3) Draw graphs on graphing paper or transparency sheets with the x and
y axis units the same for ALL graph.
4) One section of the poster board must display 3 separate overlays –
one for each trig function. You must label the axes and units on at
least one of the overlays or on the poster board. Each overlay must
have the equation of the trig function.
5) The chart below must be completed and attached to the front of your
poster or drawn and completed neatly on the front of your poster. It
may be computerized or hand written. The domain/range listed
should be only what was needed for your art work not the whole
function.
6) The bottom half of the poster should be an art work combining the 3
or more graphs. It should have a title, use at least 5 colors, and be
neat. The artwork should consume at least half of your poster board.
7) Creativity, neatness,and originality will be graded as well as content
of the design-based art output.
Function Amplitude Period
Vertical
Shift
Horizontal
Shift
Domain Range
y =
y =
y =
Modified guidelines from:
http://thefischbowl.weebly.com/uploads/6/2/8/2/62829617/trig_art_project_1.doc
3. Explain
4. Elaborate
- Brief discussion of some examples about solving situational problems involving
circular functions
Generalization ofthe Lesson:
-What are the things to be considered in solving situational problems involving

54
graphs of circular functions?
- How do you solve situational problems involving graphs of circular functions?
-What are the steps in solving situational problems on circular functions?
- In this part, the teacher and the learners will relate the terms/content/process
learned from the lesson in real life situations/scenario/instances considering the
philosophical views that can be integrated/associated to
term(s)/content/process/skills of the lesson.
Questions to be asked:
- What are the things/situations/instances that you can relate with regards to the
lesson about Situational Problems on Circular Functions?
How will you connect the terms/content/process of the lesson in real-life
Simple harmonic motion occurs when a particle or object moves back and
forth within a stable equilibrium position under the influence of a restoring force
proportional to its displacement. Simple Harmonic Motion is common in nature,
from the ups and downs of a roller coaster to the girl on a swing. The motion of a
dog’s tail and the oscillations of the strings that make up the quarks and gluons -
all these follow the simple harmonic motion.
The experiences we have in life follow a simple harmonic motion. We are
bound to encounter the ups and downs in life like the ups and downs in a roller
coaster. When we are on top, we feel happy, satisfied, and contented while when
we are in our downfall, we feel sad, dissatisfied, and discontented. As we
experience these things, we need to be resilient and optimistic.
Our experience in life can be described as a simple harmonic motion. It is
up for us to scream and enjoy the ride. In some situations, we cannot control the
track, but we do have a choice on how we will feel about the journey. We can
scream and hate it as we go back and forth, or we can throw our hands up in the
air with a beautiful smile on our face and yell out joy at the thrill of the ride.
Integration
of
Philosophical
Views
5. Evaluate
Solve the following situational problems:
a) In Canada’s wonderland there is a roller coaster that is a continuous series of
identical hills that are 18m high from the ground. The platform to get on the ride
is on top of the first hill. It takes 3 seconds for the coaster to reach the bottom of
the hill 2m off the ground .
i) Sketch a graph below which expresses the path of the roller coaster.
ii) What is the sinusoidal equation (sine and cosine) that best reflects this roller
coaster's motion?
b) A pendulum on a grandfather clock is swinging back and forth as it keeps time.

55
V. ASSINMENT
1. What are the fundamental trigonometric identities?
2. How do you establish/prove/verify problems on trigonometric identities?
Reference: DepED Pre-Calculus Learner’s Material,pages171-172
A device is measuring the distance the pendulum is above the floor as it swings
back and forth. At the beginning of the measurements the pendulum is at its
highest point, 36cm high exactly one second later it was at its lowest point of
12cm. One second later it was back to its highest position.
i) Use the information above to sketch a diagram of this sinusoidal movement.
ii) Write the sinusoidal equation (sine and cosine) that describes this situation.
c) Sam is riding his bike home from school one day and picks up a nail in his tire.
The nail hits the ground every 2 seconds and reaches a maximum height of 48 cm
(assume the tire does not deflate).
i) Use the information above to sketch a diagram of this sinusoidal movement.
ii) Write the sinusoidal equation (sine and cosine) that describes the situation
in part a.
d) At high tide the water level at a particular boat dock is 9 feet deep. At low tide
the water is 3 feet deep. On a certain day the low tide occurs at 3 A.M. and high
tide occurs at 9 A.M. Find an equation for the height of the tide at time t, where
t=3 is 3 A.M. What is the water level at 2 P.M.?

Inquiry-Based Lesson Plans in Pre-Calculus for Senior High School

Recommended

Recommended

More Related Content

What's hot

What's hot (20)

Similar to Inquiry-Based Lesson Plans in Pre-Calculus for Senior High School

Similar to Inquiry-Based Lesson Plans in Pre-Calculus for Senior High School (20)

More from Genaro de Mesa, Jr.

More from Genaro de Mesa, Jr. (11)

Recently uploaded

Recently uploaded (20)

Inquiry-Based Lesson Plans in Pre-Calculus for Senior High School