This document is a project on trigonometry by class 10 'b' students, supervised by Janak Singh Saud. It covers the definition of trigonometry, its historical context, key trigonometric ratios, and various applications in real life, particularly in astronomy. The project acknowledges the guidance of teachers and support from parents and friends in completing the work.

1. Green House
By - Class 10 ‘B’ Students
To :Mathematics Department
Supervised By: Janak Singh Saud
Exploration
in
Trigonometry
Presented By:
Aawesh Bhadra Karn
& Prabesh Kafle

2. 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.

3. Exploration On Trigonometry

4. What Is Trigonometry ?
Trigonometry (from Greek trigōnon, "triangle"and metron,
"measure")is a branch of mathematicsthatstudiesrelationships
involving lengthsand anglesof triangles.The field emergedin
the Hellenisticworld during the 3rd century BC from applications
of geometry to astronomical studies.

5. HISTORY
 Earlystudyoftrianglescanbetracedtothe 2ndmillennium BC, in Egyptianmathematics(RhindMathematicalPapyrus)
andBabylonianmathematics.
 Systematicstudyoftrigonometricfunctionsbeganin Hellenistic mathematics,reaching Indiaas partofHellenistic astronomy.
reaching IndiaaspartofHellenistic astronomy.
 In Indianastronomy,the studyoftrigonometricfunctionsflourishedin the Guptaperiod, especially due toAryabhata(sixthcentury

6. Right triangles are niceand neat, withtheir side lengthsobeying the Pythagorean
Theorem. Any two right triangles withthe same two non-rightanglesare "similar", in
the technicalsense thattheir corresponding sides are in proportion. The trigonometric
ratios are sine, cosine, tangent,cosecant, secant and cotangent.
Trigonometric ratios

7. Sin
Cos
tan
3
2
1
2
3
3
2
2
2
2
3
2
𝟑
1
2
1
1
0
0
0
∞
1
0 𝑜
30 𝑜
45 𝑜 60 𝑜
90 𝑜

8. CurveOf Sin & Cos

9. Derivationof sin 60
2a
2a
2a
Sin 60 = /2a= /2

10. 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

11. 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.

12. Thank You
Hope You Liked It !