Applications of trignometry

Applications of trignometry

1. 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.”

2. Overview Introduction History Trigonometric Function Height and Distance Architecture Astronomy Geology Navigation and Oceanography Bibliography

3. 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.

4. 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 .

5. A Trigonometric function is the ratio of certain parts of the triangle. The ratios are: Trigonometric function a c b ө A B C Sin θ = Cos θ = Tan θ = Perpendicular Base Base Perpendicular Hypotenuse Hypotenuse = = = a b c a b c Degree 30 45 60 90 Sin 1/2 1/ √2 √3/2 1 Cos 1 √3/2 1/ √2 1/2 Tan 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

6. 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.

7. 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/Hypotenuse Sin 23 = 2500/x 0.39 = 2500/x X = 2500/0.39 X = 6410 m

8. 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

9. 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.

10. 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.

11. 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.

12. 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