The concept of trigonometric ratios is important in Maths trigonometry. Some of applications and procedures are discussed here for easy understanding the concept clarity.

1. Trigonometric Ratios
Mathematics
Class VIII
Azeem Abro

2. Objectives
By the end of lesson students will be able to:
• What trigonometric ratios are
• Use trigonometric ratios to calculate a missing
angles and sides of a right triangle
• Know about trigonometric identities
• To build trigonometric values table
• Apply these to solve trigonometrical problems

3. Introduction
1
2 The branch of mathematics dealing with the relations of the sides and
angles of right triangle.
3 Trigonometric ratios: Trigonometric ratios or trigonometric functions
are the relation between two sides of right angled triangle.
4 Six ratios (sine, cosine, tangent, cotangent, secant, and
cosecant)
Trigonometry: Greek letter composed of three words tri means three,
gono means angles and metry means measurement.
Trigonometry (from Greek trigonon "triangle" + metron "measure")

4. Definitions
There are six trigonometric functions or
trigonometric ratios
Sine, cosine, tangent, cotangent, secant, and
cosecant
A hypotenuse is the longest side of a right
triangle. It's the side that is opposite to the right
angle (90°).
Perpendicular: A straight line at an angle of 90° to
a given line, plane, or surface.
Base the side adjacent to the right angle.

5. Procedure
Basically there are only three trigonometric functions, other three are the
converse of these three
1
2 CosØ: Curly Brown Hair
CosØ=
𝐵
𝐻
3 TanØ: Tin Pack Black
TanØ=
𝑃
𝐵
Hint: Remember these sentence by
recitation
SinØ: Some People Have
SinØ=
𝑃
𝐻

6. Procedure
In figure bellow,
Side AC, opposite to right angle is hypotenuse , side
opposite to angle under consideration is BC perpendicular
while AB is base of given right triangle.
A
C B
Activity, find the hypotenuse,
base and perpendicular of given figures:
A
B
C
Base
Hypotenuse
Hypotenuse
M
L
N

7. Trigonometric Identities
Trigonometric Identities are the equations used in
sum and difference of angles.
https://www.thoughtco.com

8. Applications of trigonometric ratios
Watch the link below and try to solve the remaining problem.
https://www.youtube.com/watch?v=9GUm3OJ8hss

9. Hands of activity
Use appropriate trigonometric function to evaluate the missing sides:
https://www.youtube.com/watch?v=QZc7d4TufAk
1 In above triangle ABC, side
AB=8cm making an angle at
C 450
then calculate length
of side BC, a=?
2 In above figure, m <M= 300
the
length of MN=10m, find the
measurement of m= ?
3 In above figure, find the the
missing angle x ? The height of of
triangle 25 ft and the base is 42 ft.
450
A
B C
a
8cm Base
m = ?
10m
M
N L
300

10. Extended knowledge
Tell Me How to make trigonometric ratios table ?
Step01 Write the numbers from 0 to 4
0 1 2 3 4
Step02
&03
Divide each digits by 4 and take square root
0
4
1
4
2
4
3
4
4
4
Step04 We will get trigonometric values of Sin
0
1
2
1
2
3
2
1