Application of Trigonometry

-Abhijit H Jadhav (Roll no 02 )

- Vasudev Bagal(Roll no 03 )

- Rupesh K Bandal(Roll no 04 )

“Mathematics may not teach us how to add love or minus hate. But it gives us every reason to hope that every problem

has a solution.”

Overview Introduction

History

Trigonometric Function

Height and Distance

Architecture

Astronomy

Geology

Navigation and Oceanography

Bibliography

Introduction

Trigonometry is a branch of mathematics that studies relationships between the sides and angles of triangles, particularly right triangles.

It is not only involved triangles but also involved behind how sound and light move.

The principle Trigonometric functions are sine, cosine and tangent.

It is very useful in the world of architecture, geology, astronomy etc.

History The word trigonometry is a 16th-century Latin derivative

from the Greek words for triangle (trigōnon) and measure (metron).

The origins of trigonometry can be traced to the civilizations of ancient Egypt, Mesopotamia and the Indus Valley, more than 4000 years ago.

According to Victor Katz in “A History of Mathematics (3rd Edition)” (Pearson, 2008), trigonometry developed primarily from the needs of Greek and Indian astronomers.

The Trigonometric field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies.

A Trigonometric function is the ratio of certain parts of the triangle.

The ratios are:

Trigonometric function

ac

bө A

B

C

Sinθ=Cos θ=Tan θ=

Perpendicular

Base

BasePerpendicular

Hypotenuse

Hypotenuse

=

=

= a

bca

b

c

Degree 0 30 45 60 90

Sin 0 1/2 1/√2 √3/2 1

Cos 1 √3/2 1/√2 1/2 0

Tan 0 1/√3 1 √3 ND

Cosec ND 2 √2 2/√3 1

Sec 1 2/√3 √2 2 ND

Cot ND √3 1 1/√3 0

Application of Trigonometry Find Height and distances.

In the Architecture of the buildings.

In the Astronomy

In the Geology

In the navigation purpose

In the Oceanography.

Height and distances Trigonometry is used to find the height, distance and depth of

anything easily by certain fundamentals.

Angle of elevation: It the angle made with the horizontal when the observer raises his eyes position.

Angle of depression: It the angle made with the horizontal when the observer lowers his eyes position.

It’s a very easy technique. Demonstration

Sin θ = Perpendicular/HypotenuseSin 23 = 2500/x0.39 = 2500/xX = 2500/0.39X = 6410 m

Architecture Architects use trigonometry to describe

the shapes and forms of a building using numerical equations. These equations are translated easily by any contractor to reproduce the exact building the architect had in mind.

Architects use trigonometry  to calculate structural load, roof slopes, ground surfaces and many other aspects, including sun shading and light angles.

Architecture remains one of the most important sectors of our society as they plan the design of buildings and ensure that they are able to withstand pressures from inside.

PYRAMID OF GIZA

JANTAR MANTAR

Astronomy Trigonometry was used in astronomy since ancient time.

Trigonometry is used to measure the distance to nearby stars.

In 240 B.C , a mathematician named Eratosthenes discovered the radius if the earth using trigonometry and geometry.

In 2001, a group of European astronomers did an experiment to find the distance of Venus from the Sun about 10,50,00,000 Km.

Astronomers use the method of parallax, or the movement of the star against the background as we orbit the sun, to discover new information about galaxies.

Geology Trigonometry is used in geology to estimate the true dip of

bedding angles. Calculating the true dip allows geologists to determine the slope stability.

Although not often regarded as an integral profession, geologists contribute to the safety of many building foundations.

Any adverse bedding conditions can result in slope failure and the entire collapse of a structure.

Navigation and Oceanography It is used in navigation to

find the distance of the shore from a point in the sea.

It is used in oceanography in calculating the height of tides in oceans.

Bibliography https://en.wikipedia.org/wiki/Trigonometry

http://malini-math.blogspot.in

http:// www.mathsisfun.com https:// www.mathwarehouse.com/trigonometry/ https:// www.mathportal.org https:// www.analyzemath.com/Trigonometry