math

1. Learning Objectives:
M9GE-IIIc-1
1. Illustrate the six trigonometric ratios of
special triangles.
2. Determine the six trigonometric ratios
of special triangles.
3. Appreciate the importance of
knowledge of six trigonometric ratios of
special triangles.

2. WHAT I KNOW?
.
Learning Activity 1
Directions: Complete the table below:
TRIGONOMETRIC RATIOS FOR SPECIAL RIGHT
TRIANGLE
 sin cos tan csc sec Cot
30o
450
600
𝟏
𝟐
𝟑
𝟐
𝟑
𝟑 𝟐
𝟐 𝟑
𝟑
𝟑
𝟐
𝟐
𝟐
𝟐
𝟏 𝟐 𝟐 𝟏
𝟑
𝟐
𝟏
𝟐 3
2 3
3
𝟐 𝟑
𝟑

3. WHAT’S IN?
.
Learning Activity 2:
The length of the two sides of 30o – 60o – 90o
triangle are 4 inches and 4√3 inches. Find the
length of the hypotenuse and the six
trigonometric ratios:
sin 30° = csc 30° = sin 60° = csc 60° =
cos 30° = sec 30° = cos 60° = sec 60° =
tan 30° = cot 30° = tan 60° = tan 60° =
𝟑
𝟑
𝟏
𝟐
𝟑
𝟐
𝟐
𝟐 𝟑
𝟑
𝟑
𝟑
𝟐
𝟏
𝟐
3
2 3
3
𝟐
𝟑
𝟑

4. WHAT’S IN?
.
Learning Activity 2:
Calculate the right triangle’s side lengths
whose angle is 45o and the hypotenuse is 3√2
inches. Find the trigonometric ratios.
sin 45° = _____ cos 45° = _____ tan 45° = _____
csc 45° = _____ sec 45° = _____ cot 45° = _____
𝟐
𝟐
𝟐
𝟐
𝟏
𝟐 𝟐 𝟏

5. WHAT IS IT?
.
In Geometry, the
following sides of special
right triangles are related
as follows:
450- 450 – 900 Right
Triangle Theorem in a
450- 450 – 900 triangle
300 – 600 – 900 Right
Triangle Theorem in a
300 – 600 – 900 triangle
The legs are congruent the length of the
hypotenuse is twice the
length of the shorter leg

6. WHAT IS IT?
.
The length of the
hypotenuse in 2 times of a
leg
The length of the longer leg
is 3 times the length of the
shorter leg
Hypotenuse = 2 times the
leg
Hypotenuse – 2 times the
shorter leg
Longer leg = 3 times the
shorterleg

7. .
WHAT’S MORE?
Study the following Example:
Find the length of the indicated
side.
45° 45°
m
8
m = 𝟐 ( 8)
= 8 𝟐
30°
60°
9
s
t
9 = t 𝟑
t =
𝟗
𝟑
∗
𝟑
𝟑
=
𝟗 𝟑
𝟑
= 𝟑 𝟑
s = 2t
s = 𝟐 ∗ 𝟑 𝟑 = 6 𝟑

8. .
WHAT’S MORE?
Learning Activity:
Use the theorems 30o – 60o – 90o right triangle
to solve the unknown variables x and y and find
the six trigonometric ratios.
x
4
y
sin 300 = _____ sin 600 = _____
cos 300 = _____ cos 600 = _____
tan 300 = _____ tan 600 = _____
csc 300 = _____ csc 600 = _____
cot 300 = _____ cot 600 = _____
𝟑
𝟑
𝟏
𝟐
𝟑
𝟐
𝟐
𝟑
𝟑
𝟐
𝟏
𝟐
3
2 3
3
𝟑
𝟑

9. .
WHAT’S MORE?
Learning Activity:
Use the theorems 450 – 900 – 450 right
triangle to solve the unknown variables x
and y and find the six trigonometric ratios.
sin 450 = _____
Cos 450 =_____
tan 450 = _____
csc 450 = _____
sec 450 = _____
tan 450 = _____
45°
45°
8
y
𝟐
𝟐
𝟐
𝟐
𝟏
𝟐
𝟐
𝟏

10. Assessment:
Directions: Choose the letter of the correct
answer
52°
_____ 1. Which of the following is the value of sin
600?
a.
3
2
b.
3
2
c.
3
2
d.
2
3
_____ 2. Which of the following is the value of tan
45?
a.3 b. 2 c. 1 d. 0

11. Assessment:
Directions: Choose the letter of the correct
answer
_____ 3. Which of the following have the same value
as cot 450?
a.sin 450 b. cos 450 c. csc 450 d. tan 450
_____ 4. What is the sum of sin 30 and sin 60?
a.
3+1
2
b.
3+1
2
c.
3
3
d.
4
3
_____ 5.
3
3
is also equal to…
a.sin 300 b. cos 600 c. tan 300 d. sec 600

12. Key to assessment
1. A
2. C
3. D
4. A
5. C

13. REFLECTION:
Write your personal insights about the lesson
using the prompts below.
I understand that
___________________________________________
___________________________________________
I realize that
___________________________________________
___________________________________________
I need to learn more about
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