sim-coordinates of points on the unit circle.pdf
DESCRIPTION
This Strategic Intervention Material involves "How to determine coordinates of a point in a unit circle". It is made by Mr. Roderick De Leon from Malinta National High School, Division of Valenzuela as a tool to facilitate learning during remedial classes and/or for advance studies.TRANSCRIPT
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
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REFERENCE CARD