#Introduction to trigonometry

In this session, I am going to introduce to Trigonometry.

The word trigonometry is derived from the Greek words - "Tri", "Gonia" and "metron" which means three angle measure.

This concept of mathematics is used in several fields such as Astronomy, surveying, engineering etc.

Types of angle measure:

1. Sexagesimal (English System)

2. Centesimal (French System)

3. Radian (circular)

SEXAGESIMAL MEASURE:

When we rotate a line segment about one of its endpoint, if the rotation from initial side to terminal side is 1/360th of one complete revolution, the angle measured is 1 degree.

Each part of 1 degree (1o )is divided into 60 equal parts each being called as 1 minute (1' ). Further 1 minute is divided in to 60 equal parts where each part is called as 1 second ( 1'')

CENTESIMAL MEASURE:

Here basic unit of measuring angle is grade.

1 grade (1g) = 100 minutes (1')  and 1' = 100 " (seconds)

Note: minutes and second measure of centesimal system is different from that of sexagesimal system.

RADIAN MEASURE:

One radian is the angle subtended by an arc of  length equal to its radius at its center.

One complete revolution is given by 2π radians, where pi (π) is a real number whose value is given by 22/7 

Hence, 360 degrees = 2π radians.

Relation between the three systems of Angular Measure:

Hence, if a given angle can be measured as D degrees in sexagesimal, G grades in Centesimal or C radians in Radian measure, then relation (conversion formula) between the systems of measure is given by:

D/90=  G/100=  C/(π⁄2)