Lesson plan

West Visayas State University
COLLEGE OF EDUCATION
Bachelor of Secondary Education
Major In Mathematics
Lesson Plan for Grade 9
DOUBLE-ANGLE IDENTITY FOR SINE
Prepared by: Mark Ian R. Marabe
I. Learning Objectives
During and after the period, the students must have:
A. Determined the formula of a double-angle identity for sine; and
B. Solved the exact value of the trigonometric expression using the
double-angle identity for sine.
II. Subject Matter
Topic: Double-angle Identity for Sine
Reference: Go, B.M., et. al (2013) Worktext in Trigonometry.
Materials: Manila paper, PowerPoint presentation, cartolina, colored paper,
worksheets.
Mathematical Concept:
Double-angle Identity for Sine
Formula: sin 2θ = 2sinθcosθ
Teacher's Activity
A. Daily Routine
1. Prayer
Good afternoon class. Before
we start, may we all stand and pray.
2. Cleaning
Okay class, before you sit down,
kindly pick up pieces of paper and
trash and throw them in the trash
can.
3. Greeting
Good afternoon once again. So, how
are you feeling today?
Student's Activity
A. Daily Routine
1. Prayer
The students will stand up and pray.
2. Cleaning
The students will pick up pieces of
paper and trash and throw them in
the trash can and then the students
will sit down.
3. Greeting
Good afternoon, Sir!
We're fine, Sir.

4. Checking of Attendance
Are there any absentees today?
Very good!
B. Priming
1. Recall
Before we start a new lesson, let us
have first a recap about the
previous lesson. Who can still
remember about what you have
learned with Ma'am Mendoza last
time?
Yes, Angel.
Let's hear Angel's answer.
Very good! Let us give Angel three
claps.
Last time you discussed about Sum
or Difference Identities. Now, who
can give me the formula of a sum
identity for sine?
Yes, Karl.
Let's hear Karl's answer.
Very good! Let us give Karl three
stamps.
Class, I presume that all of you are
4. Checking of Attendance
None, Sir.
B. Priming
1. Recall
Students will raise their hands.
The previous lesson that we have
discussed was all about Sum or
Difference Identities.
The students will clap their hands.
The formula of a sum identity for
sine is sin (α+β ) = sinαcosβ + cosαsinβ

already know the sum or difference
identities.
2. Motivation
Okay, class. This time I prepared a
game. This game is called "Name
the Picture." What will you do is to
guess what word is behind on the
pictures. The game will start as I
show the picture. Are you ready?
2. Motivation
Students will participate on the
game and will guess the word
based on the pictures that are
presented to them.
Yes. We are ready!
DOUBLE
ANGLE

𝟏
𝐜𝐬𝐜
C. Activity
Okay class, this time we will have an
activity. I am going to divide you into
five groups. This group (front left
side) will be the G1, this group (front
right side) will be the G2 and so on.
I am going to give each group a brown
IDENTITY
SINE
C. Activity
The students will start do the activity.

envelope. Inside of the envelope, you
can see problem. All you have to do is
to find the exact value of a particular
trigonometric expression using the
double-angle identity. You will write
your answer on the manila paper
provided. I will give you only five
minutes to finish the activity.
Group 1
1. Find the exact value of sin 60° using
the double-angle identity.
Hint: sin 2θ = 2sinθcosθ
sin 60° = sin 2(30°)
Group 2
sin 90° = sin 2(45°)
Group 3
1. Find the exact value of sin 120°
using the double-angle identity.
Possible Outcomes:
Group 1
1. sin 60° = sin 2(30°)
sin 2θ = 2sinθcosθ
sin 2(30°) = 2sin30°cos30°
sin 2(30°) = 2 (
2
1
) (
2
3
)
sin 60° = (
2
3
)
Group 2
1. sin 90° = sin 2(45°)
sin 2(45°)= 2sin45°cos45°
sin 2(45°)= 2(
√2
2
) (
√2
2
)
sin 90° = 1
Group 3
1. sin 120° = sin 2(60°)
sin 2(60°)= 2sin60°cos60°

sin 120° = sin 2(60°)
Group 4
sin 180° = sin 2(90°)
Group 5
sin 360° = sin 2(180°)
Five minutes is over. You may now
post your outputs on the board. Let us
check if they are all correct. (The
teacher will check if the student's
outputs are correct and correct them
if necessary).
Every group's answer is correct.
Very good! I think you will not be
having a hard time learning our lesson
sin 2(60°) = 2 (
2
3
) (
2
1
)
sin 120° =
2
3
Group 4
1. sin 180° = sin 2(90°)
sin 2(90°)= 2sin90°cos90°
sin 2(90°)= 2(1) (0)
sin 180° = 0
Group 5
1. sin 360° = sin 2(180°)
sin 2(180°)= 2sin180°cos180°
sin 2(180°)= 2(0) (-1)
sin 360° = 0

for today.
D. Analysis
But before we proceed to our main
topic for today, I want to call in one
representative from each group to
explain how you have arrived to such
answers.
Very good!
Let us give the representative of each
group a round of applause.
E. Abstraction
You all did great on your activity. So
now let us proceed to the discussion.
Earlier, we solved the exact value of a
certain trigonometric expression
using the double-angle identity for
sine.
Now, how did you find the exact value
of a certain trigonometric expression
using the double-angle identity for
sine? What method or strategy did you
use?
Yes, Andrei. Can you show or tell us
how it is done?
D. Analysis
The students will pick one
representative.
E. Abstraction
Yes, Sir. In order to find the exact
value of a certain trigonometric
expression using the double-angle
identity for sine, we need to divide
first the given angle by two. And then
after that, just copy or write the
formula for sine and then we will find

Very good! Let's give Andrei five
claps.
The topic that we will discuss today
is all about the Double-angle Identity
for Sine.
We all know that the formula of the
Double-angle Identity for Sine is
sin 2θ = 2sinθcosθ . Now, where do we
get this formula? Who has an idea
where do we get this one?
Okay. The formula of Double-angle
Identity for Sine is sin 2θ = 2sinθcosθ ,
right?
The formula comes from this
equation...
sin ( α + β ) = sinαcosβ + cosαsinβ
And we will assume that these two
Greek letters (α and β) will equal to θ.
And after that, we will have this kind
of equation...
sin (θ + θ) = sinθcosθ + cosθsinθ
And combine like terms, we have:
the theta or angle. And after that we
will find the exact value of a certain
trigonometric expression and after
that just do some computation.
No one raising their hands.
Yes, Sir.

sin 2θ = 2sinθcosθ .
In order to appreciate this formula, we
will try some examples.
Solution:
sin 60° = sin 2(30°)
sin 2(30°)= 2sin30°cos30°
sin 2(30°)= 2 (
2
1
) (
2
3
)
sin 60° =
2
3
Are there any questions?
Do I made it clear?
Now, who can answer this kind of
problem.
Anyone from the class?
Yes, Rowela. Let's hear Rowela's
answer. (Rowela will go to the board
and solve the problem and after that
she will explain her answer. While
Rowela is solving on the board, the
other students will solve also.
Very good, Rowela!
None, Sir!
Yes, Sir!
Students are raising their hands.

Let's give Rowela three claps.
How about if our theta lies in a
specific quadrant, what shall we do?
How can we find the exact value of a
given trigonometric expression if our
theta lies in a specific quadrant?
Who has an idea?
Okay. Let's give an example.
3. If sin θ=
4
5
and θ lies in a Quadrant I,
find the exact value of sin 2θ.
Solution:
sin θ=
4
5
=
y
r
Solving for x, using the Pythagorean
Theorem.
x2
+ y2
= r2
x2
+ 42
= 52
x2
= 52
- 42
x = √25− 16
x = √9
x = 3 In Q1, x is positive
So, cos θ =
3
5
=
x
r
Then sin 2θ = 2sinθcosθ
sin 2θ = 2 (
4
5
) (
3
5
)
sin 2θ = 2 (
12
25
)
sin 2θ =
24
25
Verifying or checking the obtained
No one raising their hands.

value.
If sinθ =
4
5
θ = sin−1
(
4
5
)
θ = 53°7'48"
Substitute in sin 2θ
sin 2θ
sin 2(53°7'48")
sin 106°15'36"
Are we clear, class?
How about this one.
4. . If sin θ = and lies in a Quadrant II,
find the exact value of sin 2θ .
Anyone from the class?
Yes Raine.
Let's hear Raine's answer. (Raine will
go to the board
and solve the problem and after that
she will explain her answer. While
Raine is solving on the board, the
other students will solve also.
Very good, Raine!
Let's give Raine three claps.
How about if we encounter this kind
of problem. (The teacher will point
the problem number 5). How could we
solve this? How could we find the
exact value of a certain trigonometric
expression using double-angle
Yes, Sir!
The students are raising their hands.

identity? Who has an idea?
5. Find the exact value of
sin30°cos30° using double-angle
identity.
Yes, Jasmine.
Verifying the obtained value:
sin30°cos30° =
2
3
This time, try to solve this.
6. Find the exact value of
sin60°cos60° using double-angle
identity.
Anyone from the class who would like
to answer this kind of problem. Who
wants to solve the problem on the
board?
Yes, Sophia. (Sophia will solve on the
board while the other students will
solve also in their seats. After
solving, Sophia will explain her
answer).
Solution:
sin30°cos30° = (2sin30°cos30°)
sin30°cos30° = sin 2(30°)
sin30°cos30° = sin 60°
sin30°cos30° = (
2
3
)
Solution:
sin60°cos60° = (2sin60°cos60°)
sin60°cos60° = sin 2(60°)

Very good, Sophia.
Let's give Sophia three claps.
F. Generalization
Are there any questions?
So let's have a review of what we
discussed.
What is the formula in finding the
exact value of a certain trigonometric
expression in double-angle identity
for sine?
Yes, Vinz.
Let's hear Vinz' answer.
Very good, Vinz.
Let's give Vinz three claps.
Okay. How about if our theta lies in a
certain quadrant, how could we find
the exact value of certain
trigonometric expression? What shall
we do?
Yes, Julisha.
Let's hear Julisha's answer.
sin60°cos60° = sin 120°
sin60°cos60° = (
2
3
)
F. Generalization
None, Sir.
The formula in finding the exact value
of a certain trigonometric expression
in double-angle identity for sine is
If this is the case, we need to graph
first the given value of our theta in a
certain quadrant. And after that, we

Very good, Julisha.
Let's give Julisha three stamps.
Alright. You really understood the
lesson well. Are there any more
questions about our lesson?
G. Assessment
Read each direction and answer the
following.
I. Use the sine of a double-angle to
find the exact value.
1. sin π
will use the Pythagorean Theorem in
order to find the other theta. And then
if we have now the values, just do
some substitution and now compute.
That's all!
None, Sir.
G. Assessment
Possible Answers
I.
1. sin π = sin 90°
sin 90° = sin 2(45°)
sin 2(45°) = 2sin45°cos45°
sin 2(45°) = 2 (
√2
2
) (
√2
2
)
sin 90°= 1

II. Write each expression as a sine of
a double-angle, then find the exact.
1. sin20°cos20°
H. Assignment
A. Use the sine of a double-angle to
find the exact value of
1. sin π
B. What are the formulas of a
double-angle identity for cosine?
Goodbye class. See you tomorrow.
II.
1. sin20°cos20° = (2sin20°cos20°)
sin20°cos20° = sin 2(20°)
sin20°cos20° = sin 40°
Goodbye and thank you Sir.
See you around.

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