A Strategic Intervention Material

Mathematics IV

Malinta National High School

TITLE CARD

Least Mastered Learning Competency: Determine the coordinates of the Points on the

Unit Circle

Subtasks:1. Identify the Reference angle of a given angle.

2. Locate the quadrant in which the terminal side of

the given angle terminates.

Help!...help!!!

The zombies are running

after me. They’re going to

eat my brain once they

catch me and have no

answer to their question

They’re asking

about the

coordinates of

225?

Harr…harr…haaarrrr

What’s

wrong

plant?

What was their

question?

Ok…I’ll help you find

the solution to your

problem before it’s too

late.

Let’s Go

GUIDE CARD

Before we proceed… I’ll transform first to discuss you more in detail

Let’s discuss first the following terms which will be needed to

determine the coordinates of the angle on the unit circle.

Here all angles are in standard position. Angle in standard position are

angles whose initial sides lie on the positive x-axis.

Every angle in unit circle can be expressed as function P() = (x, y).

P(30) = (3/2, 1/2) P(45) = (2/2, 2/2) P(60) = (1/2, 3/2)

Just remember the coordinates of those special angles huh…Because you

will be using them later.

Ok….Gotcha So…Let’s continue

The following are special angles with their coordinates:

Now take a look at the angle below in unit circle, what do you

observe?

The angle is equal to120 …it is not anymore a special angle…! What

will we do now?

Wait! I will transform to think deeper…

Ok…I am very excited to meet him and ready to do the exercises.

My friend Crazy Dave will give some exercises for you on reference

angle.

120

Aha! Let us use its reference angle.

Reference angle is a positive acute angle between

the x-axis and the terminal side of the given angle.

Remember:

Positive angle rotates Counterclockwise while

Negative angle rotates Clockwise.

Therefore, reference angle of 120 is 60.

Better if I will be in my normal me this time…

60

1. 150

4. 225

2. 60

5. 330

3. -120

Hi I am Crazy Dave!

Are you ready for this

activity?

Activity #1:

Identify the reference angle of the

following.

Answer: _____

Answer: _____

Answer: _____

Answer: _____ Answer: _____

ACTIVITY CARD

This time we are going to locate the quadrant the given

angle terminates.

1. 150 2. 60 3. -120 4. 225

5. 330 6. -30 7. -110 8. 368

Questions:

1. Which of the angles are located in a) QI _________ b) QII __________

c) QIII ___________ and d) QIV ____________?

2. What are the signs of coordinates of angles terminate at QI, QII, QIII

and QIV? __________________________________

Here we go again…let’s locate

the quadrant each angle

terminates.

Activity #2:

At what quadrant could you find the terminal side of each angle to the

right?

Answers:

1. ____ 2. ____ 3.____ 4. ____ 5. ____ 6. ____ 7. ____ 8. ____

Now I guess you know already the important terms to be considered

in determining the coordinates of the angles on a unit circle. Try the

next activity to enhance your knowledge on the concept.

Given Angle

Reference angle/ Coordinates

Quadrant/ Coordinates of the given angle

1. 150 ___________ ____________

2. 60 ___________ ____________

3. -120 ___________ ____________

4. 225 ___________ ____________

5. 330 ___________ ____________

Activity #3:

Fill in the blank with the correct answer.

30 / (3/2, 1/2) QII / (-3/2, 1/2)

Questions:

1. How will you relate coordinates of the given angle and coordinates of

its reference angle?__________________________________________

2. What do we consider in determining the coordinates of the angles in

unit circle? _________________________________________________

Fine and …Great!

Yup! I owe you my life.

Thank you very much

for sharing your ideas.

Now I can face the

zombies with

confidence.

It’s alright! Just call me once

you need my help.

Before you leave, answer the last

activity for you to evaluate your

understanding with the concept.

How’ s your feeling…Plant?

Do you know already how to

determine the coordinates of

the angles in a unit circle?

ASSESSMENT CARD

315

-30240

-120

135

390

(3/2, -1/2)

(3/2, 1/2)

(-1/2, 3/2)

(-1/2, -3/2)

(-2/2, 2/2)

(2/2, -2/2)

I call this activity...S-MATCH DOWN

Match the circular figure with the rectangular figure by using

an arrow to determine the correct coordinates of each angle.

Stop… Look… and Read More…

Every angle corresponds to a distinct coordinates (x, y)

of point on the unit circle. This means P() = (x, y).

1. Direction of rotation of the angle in standard position

2. The quadrant in which the terminal side of the angle

terminates

3. Its reference angle and magnitude of its coordinates.

To determine the coordinates of the angle on

the unit circle, the following are to be considered

1./3 ______

2./4 ______

3./6 ______

4.5/3 ______

5.-7/4 ______

Determine the coordinates of the following

angles in radian measures.

ENRICHMENT CARD

Dilao, Soledad J., Orines Fernando B., & Bernabe, Julieta G.

(2009). Advanced Algebra, Trigonometry and Statistics.

Department of Education, Republic of the Philippines

Landicho, Elizabeth D. C. (2005). MSA Trigonometry. MSA

Academic Advancement Institute

Ayres, Frank Jr. A. & Robert E. Moyres (1999). Theory and

Problems of Trigonometry, Third Edition: Schaum’s Outline

Series, McGraw-Hill Companies Inc.

Chua, Simon L., et al (1996). 21st Century Mathematics Fourth

Year. Phoenix Publishing House

WWW. GOOGLE.COM & WWW. YAHOO.COM. Images Search

Engines

REFERENCE CARD

ANSWER KEY