# Introduction

The term trigonometry has its origin from the Greek word trigonon meaning triangle and metron meaning a measure.

The word trigonometry is developed from the study of right triangles by applying the relationships between the measures of its sides and its angles to the study of similar triangles.

However, the word "trigonometry" did not exist upon the birth of the subject, but was later introduced by Bartholomaeus Pitiscus the German mathematician and astronomer.

It was originally developed as a means of computing unknown sides and angles of triangle and the related figures by the early Greeks, especially by the mathematician Hipparachus (180 â€“ 125 BC).

**Hipparachus (180 â€“ 125 B.C.) **

Claudius Ptolemy worked further on Hipparchus' chord table and came up with a more complete one. He used Euclid's propositions to aid in his work and developed a method of calculating square roots, though he never explained how. Using his theorem (for a quadrilateral inscribed in a circle, "the product of the diagonals equals the sum of the products of the opposite sides") and the half-angle formula, he derived the sum and difference (addition) formulae.

**Claudius Ptolemy**

# Trigonometry and its Types

The branch of mathematics which deals with the relationships between the sides and angles of triangles and also with the properties and applications of the trigonometric functions of angles is known as Trigonometry.Â

They are broadly classified into two types, one is plane trigonometry, which deals with figures lying wholly in a single plane

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and the other is spherical trigonometry, which deals with triangles that are sections of the surface of a sphere.

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From the figure, the yellow shaded region is a spherical triangle formed by the intersection of the three circles.

# Various Application of Trigonometry

1. The various fields of applications of trigonometry are used in astronomy, navigation, and surveying. It also plays an important role in determing distance, such as the distances of the stars and planets from the earth, or of a distance that could not be measured directly, such as the distance across a large lake.Â

Distance between Earth and Moon

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**Distance between the Stars from the Earth **

2. Trigonometry is extensively used in calculus, in the study of wave motion, vibration, alternating current and sound etc.

3. Other applications of trigonometry are used in various branches of engineering, also particularly in the study of periodic phenomena, such as vibration studies of sound, a bridge, or a building, measuring distances across rivers, computing mountain heights, etc.

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Â **Bridge**

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**Building**