Trigonometry is a mathematical branch focused on the relationships between distances and heights, derived from Greek terms for three, sides, and measure. It dates back to usage by early astronomers in Egypt and Babylon for celestial measurements. The document outlines trigonometric ratios, common angle values, and key identities.

1. Trigonometry
By Sukhnoor Singh Gill

2. What is Trigonometry
Trigonometry is a branch of Mathematics that
deals with the distances or heights of objects
which can be found using some mathematical
techniques. The word 'trigonometry' is derived
from the Greek words 'tri' (meaning three),
'gon' (meaning sides) and 'metron' (meaning
measure).

3. Early use of
Trigonometry
The earliest known work
on trigonometry was
recorded in Egypt and
Babylon. Early
astronomers used it to find
out the distances of the
stars and planets from the
Earth.

4. Trigonometry Ratios
There are 6 Trigonometry Ratios
Sin θ Side Opposite to θ/Hypotenuse
Cos θ Side Adjacent to θ/Hypotenuse
Tan θ Side Opposite to θ/Side adjacent to θ
Cosec θ Hypotenuse/Side Opposite to θ
Sec θ Hypotenuse/Side Adjacent to θ
Cot θ Side adjacent to θ/Side Opposite to θ

5. Trigonometric values of some common angles
Trigonometry Ratios Table
θ 0° 30° 45° 60° 90°
Sin θ 0 1/2 1/√2 √3/2 1
Cos θ 1 √3/2 1/√2 1/2 0
Tan θ 0 1/√3 1 √3 ∞
Cosec θ ∞ 2 √2 2/√3 1
Sec θ 1 2/√3 √2 2 ∞
Cot θ ∞ √3 1 1/√3 0

6. Trigonometric Identities
Sin2θ +
Cos2θ = 1
1 - Sin2θ
= Cos2θ
1 - Cos2θ =
Sin2θ
Cot2θ + 1
= Cosec2θ
Cosec2θ -
Cot2θ = 1
Cosec2θ -
1 = Cot2θ
Tan2θ + 1 =
Sec2θ
Sec2θ -
Tan2θ = 1
Sec2θ - 1
= Tan2θ