## Introduction:

The initial history of trigonometry is linked with GREEK. HIPPARCUS was the first person who tabulate the values of ARC and CORD for a series of angles. He is known as the “father of trigonometry”.

Trigonometry comes from a Greek “trigonon” means “triangle” and “metron” means “to measure”. Trigonometry is a branch of mathematics which shows relationship between the length of sides of triangle and its angles.

Basic trigonometry refers to a triangle especially a right-angle triangle

Capital letters A, B, C refers to angles while small letters a, b, c refers to sides of a triangle. So, we can say that a triangle has six parts; three sides and three angles. So, trigonometry means measurement of its sides and angles. In case of right-angle triangle there is a fixed ratio between angles and sides so we can easily determine any unknown value of triangle by trigonometric ratios.

## Basic trigonometric ratios:

Three basic trigonometric ratios are as follows:

\text { Sine } \theta=\frac{\text {Perpendicular}}{\text {Hypotenuse}}\text { Cosine } \theta=\frac{\text { Base }}{\text { Hypotenuse }}
\text { Tangent } \theta=\frac{\text { Perpendicular }}{\text { Base }}

## Applications of trigonometry:

Trigonometry is used in different fields of life in various aspects, some of them are as follows:

## In developing computerized music:

We all know that music is a form of sound and sound travel in the form of wave. Hence a computerized music is also developed by using sine and cosine values of trigonometric functions.

Navigation is a procedure in which we study about the position and direction of any moving body on or above the Earth. It can be any type of navigation depending upon position of object i.e. marine navigation, land navigation or space navigation. So, in case of marine navigation position and direction of boat or ship can be determined by taking the values from compass and pinpoint poles (light house) in the sea. This can be done by using basic trigonometric ratios.

## In developing computerized music:

We all know that music is a form of sound and sound travel in the form of wave. Hence a computerized music is also developed by using sine and cosine values of trigonometric functions.

## Trigonometry in video games:

While making video game the jumps of a character are made by using trigonometric ratios. As jumpy position is in the form of a parabolic motion hence by making a triangle the direction and height of jump can be determined.

## Inclined roofing of a house:

In case of single-story house when the roof is made inclined its slope is determined by trigonometry.

As total width of the house is 12ft so half of it is the value of base.

\text { Base }=a=\frac{12}{2}=6 f t

Now we have come to know about the value of base (a=6ft)          and the perpendicular (b=3ft). The tangent will be

\tan \theta=\frac{\text {perpendicular}}{\text {base}}=\frac{b}{a}=\frac{3 f t}{12 f t}=0.25 f t

To find out angle θ shift tangent on right side i.e. inverse of tangent.

= tan-1 0.25
Θ = 14

So, the angle of the roof should be 140.

## Trigonometry in map creation:

Trigonometry is used in map creation of city as well as a country or even world. In world mapping longitudes and altitudes, location of continents and subcontinents along with north and south pole is to be mentioned by using trigonometric ratios. As we should have knowledge about directions, angles and distances so these values can be found out by using trigonometric ratios.