Green HouseBy - Class 10 ‘B’ Students To :Mathematics Department

Supervised By: Janak Singh Saud

Exploration in

Trigonometry

Presented By: Aawesh Bhadra Karn& Prabesh Kafle

Acknowledgement

I would like to express my special thanks of gratitude to my Optional Maths teacher  Mr. Janak singh Saud as well as our principal  Mahendra Khanal who gave us the golden opportunity to do this wonderful project on the topic Trigonometry , which also helped me in doing a lot of Research and  we came to know about so many 

new things we are really thankful to them.

Secondly we would also like to thank our  parents and friends who helped us  a lot in finalizing this project within the limited time frame.

Exploration On Trigonometry

What Is Trigonometry ?

Trigonometry (from Greek trigōnon, "triangle" and metron, "measure") is a

branch of mathematics that studies relationships involving lengths and

angles of triangles. The field emerged in the Hellenistic world during the 3rd

century BC from applications of geometry to astronomical studies.

HISTORY Early study of triangles can be traced to the 2nd millennium BC, in Egyptian

mathematics (Rhind Mathematical Papyrus) and Babylonian mathematics.

Systematic study of trigonometric functions began in Hellenistic mathematics, reaching India as part of Hellenistic astronomy.

In Indian astronomy, the study of trigonometric functions flourished in the Gupta period, especially due to Aryabhata (sixth century CE).

During the Middle Ages, the study of trigonometry continued in Islamic mathematics, hence it was adopted as a separate subject in the Latin West

The development of modern trigonometry shifted during the western Age of Enlightenment, beginning with 17th-century mathematics (Isaac Newton and James Stirling) and reaching its modern form with Leonhard Euler (1748).

Right triangles are nice and neat, with their side lengths obeying the Pythagorean Theorem. Any two right triangles with the same two non-right angles are "similar", in the technical sense that their corresponding sides are in proportion. The trigonometric ratios are sine, cosine, tangent, cosecant, secant and cotangent.

Trigonometric ratios

Trigonometric values of some angles

Sin

Cos

tan

√32

12

√33

√22

√22

√32

√𝟑

12

110

00∞

10𝑜 30𝑜 45𝑜60𝑜 90𝑜

Curve Of Sin & Cos

Derivation of sin 60

2a

2a

2a

Sin 60 = /2a= /2

Trigonometry is commonly used in finding the height of towers and mountains.

It is used in navigation to find the distance of the shore from a point in the sea.

Application of trigonometry in real life

Application of Trigonometry in Astronomy

I. Since Ancient times trigonometry was used in astronomy.

II.The technique if triangulation is used to measure the distance to nearby stars.

III.In 204 B.C a mathematician named Eratoshenes discovered the radius of the Earth using trigonometry and geometry.

IV.In 2001 , a group of European Astronomers did an experiment that started in 1997 about the distance of Venus From the sun . Venus was about 105,000,000 kilometers away from the sun.

Thank

YouHope You Liked It !