This document provides an introduction to trigonometry, including definitions of key terms like hypotenuse, perpendicular, and base in the context of a right triangle. It explains Pythagoras' theorem that the sum of the squares of the legs of a right triangle equals the square of the hypotenuse. Trigonometric ratios like sine, cosine, and tangent are also defined in terms of the sides of a right triangle. An example problem demonstrates using trigonometric ratios and Pythagoras' theorem to solve for a missing side of a triangle.

1. By : Ayushi Sharma

2. Introduction to Trigonometry
It is made up of two Greek words trigonon and
metron.
Trigonon – Triangles or three angles
Metron - Measurement

3. Right triangle
• A triangle in which anyone angle is
equal to 90 0 is called a right triangle.
• Other angle will be denoted by θ.
• The side opposite to the right angle
is known as hypotenuse.
In ∆ABC, side AC is hypotenuse.
• The side opposite to θ is known as perpendicular.
In ∆ABC, side AB is perpendicular.
• The adjacent side to θ is known as base.
In ∆ABC, side BC is base.

4. Pythagoras Theorem
According to Pythagoras theorem , the sum of
square of adjacent sides of right angle is equal to
square of side opposite to right angle.
In ∆ABC,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
H = √P2+B2
i.e. AC2 = AB2 + BC2

5. Example :
Calculate the hypotenuse of the triangle with sides of 3cm and 4 cm.
Solution: Given, a = 3 cm
b = 4 cm
c = ?
By Pythagoras theorem,
H2 = P2 + B2
c2 = a2 + b2
c2 = 32+ 42
c2 = 9 + 16
c 2= 25
c = √25
c = 5cm
Therefore hypotenuse c is 5 cm .
In this way we can find out any of the three sides .
p
r
q
a= 3 cm
b=4cm
c =?

6. Trigonometric Ratios
The Trigonometry Ratios of the angle θ
in the ∆ ABC are defined as follows.
Sine θ = P∕H → sin
Cosine θ = B ∕ H → cos
Tangent θ = P ∕ B → tan
Following ratios are the opposites of above ratios.
Cosecant θ = H ∕ P → cosec
Secant θ = H ∕ B → sec
Cotangent θ = B∕ P → cot
Mnemonics to learn these ratios –
Some People Have, Curly Black Hair Through Proper Brushing.
Here, Some People Have is for
Sin θ= P/ H
Curly Black Hair is for
Cos θ= B/ H
Through Proper Brushing is for
Tan θ= P/B

8. Example :
If tan A = 2/3 then find out rest of the ratios.
Solution: Given , tan A = 2/3
As we know that tan A = P/B
So , P= 2 and B = 3
By Pythagoras theorem
H =√22+3 2
H = √4 +9
H = √13
Sin A= P/H = 2 /√13
Cos A = B/H = 3/√13
Cosec A = H/ P =√1/2
Sec A= H/ B = √13/3
Cot A = B/P = 3/2