DETAILED LESSON PLAN IN MATHEMATICS 9
I. OBJECTIVES
The learner demonstrates understanding of the basic concepts of
Content Standards
trigonometry.
Performance The learner is able to apply the concepts of trigonometric ratios to
Standards formulate and solve real life problems with precision and accuracy.
Specific Learning Illustrate the six trigonometric ratios: sine, cosine, tangent, secant,
Objectives/Learning cosecant, and cotangent.
Competencies
II. SUBJECT MATTER
Topic: Triangle Trigonometry
Sub topic: The six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent.
Materials: Activity sheets, ruler, protractor, visual aids
References:
III. LEARNING PROCEDURE
Teacher’s Activity Student’s Activity
A. Preliminary activities Our Father, Who art in heaven, hallowed be Thy
name; Thy kingdom come; Thy will be done on
1. Prayer earth as it is in heaven. Give us this day our daily
Please stand up and let us pray. Jonas may you lead the bread; and forgive us our trespasses as we forgive
prayer.
those who trespass against us; and lead us not into
temptation, but deliver us from evil.
Good morning sir.
2. Greetings
Good morning class!
3. Checking of Attendance No one is absent today sir.
Our class secretary, is there any absent today?
Very Good!
4. Review
But before we proceed with our new lesson, let us first Sir, our previous lesson was all about the
recall the topic that we had the last meeting, anyone Pythagorean Theorem
from the class who has a good memory from the
discussion?
Very good, anyone who can tell me something about
the theorem?
Sir, the length of the hypotenuse is equal to the
square root of the sum of the square of two legs. Or
we have…
Excellent! c2 = a2 + b2
From the triangle given here can you identify the legs Sir we have
of which is the opposite and the other is the adjacent,
the angle, and the hypotenuse.
a c
.
ϴ
b
Where, leg a as the opposite side, leg b as the
adjacent side, c as the hypotenuse and ϴ as the
5. Motivation reference angle.
TRIVIA
Class, we know that triangle comes in many
flavors, there are equilateral, Isosceles, scalene, right,
obtuse and acute triangles. Don’t you know the triangle
is the strongest shape? If you try to create a shape out
of sticks joined with hinges for example square even
without force applied it will be transformed into a
parallelogram but triangles will not, For a triangle,
no matter what type, this can’t happen. It’s inherently
rigid. That’s why this shape is very common on
buildings and other construction.That’s why some
build landmarks like this.
Yes sir!
It’s how important this shape is.
Would you like to know more about triangles?
Very good.
6. Drill Spelling words.
Before we proceed to our lesson let us have first an
activity. 1.Trigonometric ratio
2.Adjacen
Spelling words. 3.Hypotenuse
4.Cotangent
1.Trigonometric ratio 5.Cosine
2.Adjacen 6. Sine
3.Hypotenuse
4.Cotangent
5.Cosine
6. Sine
B. Lesson Proper
1.Presentation of the topic
Yes, Sir
Class, before we can build or create the triangle
that we desire we need to determine and solve its
measurements such as sides and angles. Do you agree
Yes, Sir. We can solve it using the
guys?
Pythagorean Theorem.
Very good.
Of course, we know already how to solve for the
sides right? Not yet Sir!.
Yes, very good. Sir it’s all about solving the measurements of an
angle in a triangle.
But can we solve the measurement of angles using the
theorem?
Then, anyone who knows already of the topic this Our objective this morning are:
morning? 1.illustrate the six trigonometric ratios: sine,
cosine, tangent, secant, cosecant, and cotangent,
Very good.
1.1. determine relationship between the
Our topic this morning is about solving measurements trigonometric ratios and their equivalence.
of a triangle with the use of the six trigonometric 1.2.draw triangles illustrating the six
ratios. But before we formally start the discussion let trigonometric ratios, and
us first set our objectives. Please read anyone? 1.3. relate the six trigonometric ratios into real life
situations.
Yes Sir!
Do you think we can attain our objectives for today?
Fantastic
2.Discussion
Let us have this illustration
c
a
ϴ
b
In solving triangles given an angle ϴ and the legs, we
use the ratios represented by the mnemonics SOH
CAH-TOA where this represents the relationship
between the parts of the triangle using Sine, Cosine
and Tangent ratios. CHO SHA CAO for cosecant,
secant, and cotangent ratios.
First is SOH, it stands for Sin ϴ = Opp/Hyp or we
read it as Sine Theta is equal to opposite over
hypotenuse.
Sir, we have side a as our opposite and c as
the hypotenuse then,
Based on the given illustration who will
identify and write the equation using Sin ϴ = a/c
the opposite and the hypotenuse side
in the Mnemonic SOH.
Very good,
In the Cosine ratio represented by mnemonic CAH and
Tangent as TOA where:
C = Cosine Theta
A = Adjacent side
H = Hypotenuse
T = Tangent
Sir, just like the first ratio for sine where a
O = Opposite
as the opposite side, b as the adjacent and c as
Based on the illustration on the board, who will write the hypotenuse we have:
the exact ratio for Cosine and Tangent?
For the cosine ratio:
Cos ϴ = b/c
And for the tangent ratio:
Tan ϴ = a/b
Fantastic, these ratios are very important to remember
because this will help you solve measurement of the
triangle given only limited information e.g. sides and
angles. None Sir!
Any questions class?
Very good
C.Application
Class, I’m going to divide the class into three groups
and we are going to solve together each problem
assigned within the group.
Class, as we solve the problems please be guided with
the following criteria to be used during the activity.
DISTIN PROFI APPRE NOVIC
GUISH CIENT NTICE E-1
ED - 4 - -
3 2
Underst
ands the
Problem
Republic of the Philippines
Department of Education
National Capital Region
DIVISION OF CITY SCHOOLS
CALOOCAN CITY
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