This document summarizes a student project on trigonometry. It was created by a class of 10 students along with their math teacher to help students learn trigonometry through practical experiments and research. The project covers the basics of trigonometry including definitions, history, applications like measuring inaccessible heights, and examples of using trigonometric functions and identities to solve problems.

1. TRIGONOMETRY..

2. YELLOWHOUSE
CLASS“10 B”
MEMBERS: DEWAMSHBASYAL
RITUSHA KHADKA
NISHAN POUDEL
AMIC RAI
RIVIKA LAMSAL
NIKITA THAPA
MATHS DEPARTMENT
Collaboration with: Janak Singh Saud
Math's teacher

3. PRESENTED BY:
DEWAMSHA BASHYAL
AND
RITUSHA KHADKA

4. THIS PROJECT IS CREATED IN ORDER TO HELP THE STUDENTS TO LEARN THE TOPIC TRIGONOMETRY AND BY
PRACTICAL RESEARCH AND EXPERIMENTS. THIS PROJECT IS BASED ON “LEARN BY DOING” AGENDA. WE WANT
TO THANK OUR SCHOOL, ESPECIALLY THE MATH DEPARTMENT TO PROVIDE US THIS FABULOUS LEARNING
OPPORTUNITY. THIS PROJECT IN CREATED IN THE COLLABORATION OF YELLOW HOUSE STUDENTS OF CLASS 10
B ALONG WITH THE OPTIONAL MATHEMATICS TEACHER MR. JANAK SINGH SAUD. WE WANT TO THANK HIM,
OUR PARENTS AND THE WHOLE SCHOOL FOR THIS.
Acknowledgement

5. LETS KNOW……
Trigonometry is the
branch of
mathematics
which deals with the
measurement of

6. 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).

7. This is
pretty
easy!
BASE (B)
PERPENDICULAR(P)
Trigonometric
ratios...

8. TRIGONOMETRIC VALUES OF SOME
ANGLES...
 A 0  3 0  4 5  6 0  9 0 
Sin A 0 1
Cos A 1 0
Tan A 0 1 Not
Defined
Cosec A Not
Defined
2 1
Sec A 1 2 Not
Defined
Cot A Not
Defined
1 0

9. TRIGONOMETRIC
IDENTITIES...
Sin2  + Cos2  = 1
• 1 – Cos2  = Sin2 
• 1 – Sin2  = Cos2 
Sec2  - Tan2  = 1
• Tan2  + 1 = Sec2 Sec2  - Tan2  = 1
• Sec2  - 1 = Tan2 
Cosec2  - Cot2  = 1
• Cot2  = 1+Cosec2 
• Cosec2  - 1 = Cot2 

10. POWER OF TRIGONOMETRY...
• HISTORICALLY, IT WAS DEVELOPED FOR ASTRONOMY AND
GEOGRAPHY, BUT SCIENTISTS HAVE BEEN USING IT FOR
CENTURIES FOR OTHER PURPOSES, TOO. BESIDES OTHER FIELDS
OF MATHEMATICS, TRIGONOMETRY IS USED IN PHYSICS,
ENGINEERING, AND CHEMISTRY. WITHIN MATHEMATICS,
TRIGONOMETRY IS USED PRIMARILY IN CALCULUS (WHICH IS
PERHAPS ITS GREATEST APPLICATION), LINEAR ALGEBRA, AND
STATISTICS. SINCE THESE FIELDS ARE USED THROUGHOUT THE
NATURAL AND SOCIAL SCIENCES, TRIGONOMETRY IS A VERY
USEFUL SUBJECT TO KNOW.
What can we
do?

11. APPLICATION…
•MEASURING INACCESSIBLE
LENGTHS
• HEIGHT OF A BUILDING
(TREE, TOWER, ETC.)
• WIDTH OF A RIVER

12. USE OF CLINOMETER
• CLINOMETERSIS A DEVICEWHICH ISUSEDTOMEASURETHE
ANGLEOFELEVATIONAND DEPRESSIONWHICH HELPSTO
FINDTHEHEIGHT ORDISTANCEOFDIFFERENTOBJECTS.

13. OTHER APPLICATIONSOF TRIGONOMETRY...
ACOUSTICS,
SPORTS,
 ARCHITECTURE,
 ASTRONOMY,
 CARTOGRAPHY,
CIVIL ENGINEERING,
GEOPHYSICS,
CRYSTALLOGRAPHY,
ELECTRICALENGINEERING,
ELECTRONICS,
PROBABILITYTHEORY,
MECHANICAL ENGINEERING,
 MACHINING,
 MEDICALIMAGING,
NUMBERTHEORY,
OCEANOGRAPHY,
 OPTICS,
SEISMOLOGY,
STATISTICS,
 VISUALPERCEPTION
 LANDSURVEYINGANDGEODESY,
 PHYSICALSCIENCES,

14. HOW TRIGONOMETRY IS USED IN SPORTS.
Basketb
all

15. TRIGONOMETRY IN
BASKETBALL...
THE BALL HAS THE HIGHEST PERCENTAGE OF GOING IN THE BASKET
AT AN ARC RATHER THAN OVER HAND AND STRAIGHT.
PHYSICS PROFESSOR PETER BRANCAZIO ESTABLISHED THE OPTIMUM
ANGLE FOR THE SHOT IS 45 DEGREES.
THIS ANGLE MAY VARY ON HEIGHT OF THE PLAYER SINCE IF A TALLER
PLAYER GOES TO THE LINE COMPARED WITH A SHORTER, THE IDEAL
ANGLE WILL CHANGE.

16. TRIGONOMETRY IN GOLF...
• GOLF INVOLVES
TRIGONOMETRY AS THE
GOLFER NEEDS TO
DETERMINE A SPECIFIC
ANGLE TO WHICH HE WILL
HIT THE BALL IN ORDER
FOR IT TO REACH ITS
FINAL DESTINATION.

17. TRIGONOMETRICRATIOS...
Whenβ=90°
β
X
A
C
Y
O
X’
Y’
B
IN THIS FIGURE,
WHEN OB REACHES OC
β=90°
BA = OC/OB
OABECOMES O
SO,
IN OAB
HYPOTENUSE(OB)=1(LET)
BASE(OA)= 0
PERPENDICULAR(BA) = 1

18. THE VALUES OF THE TRIGONOMETRIC RATIOS
ARE...
Sinβ=
𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
1
1
=1
Cotβ=
𝐵𝑎𝑠𝑒
𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
=
0
1
=0
Secβ=
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝐵𝑎𝑠𝑒
=
1
0
=
∞
Cosecβ=
=
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
1
1
=1
Cosβ=
𝐵𝑎𝑠𝑒
𝐻𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
=
0
1
=0
Tanβ=
𝑃𝑒𝑟𝑝𝑒𝑛𝑑𝑖𝑐𝑢𝑙𝑎𝑟
𝐵𝑎𝑠𝑒
=
1
0
=∞

19. CAST RULE...
C
S
T
ASIN
COSE
C
COS
SEC
TAN
COT
ALL

20. THIRD QUADRANT...
X
Y
X’
Y’
-y
r
-x
Cosβ=
𝐵
𝐻
=
−𝑥
𝑟
=-
Sinβ=
𝑃
𝐻
=
−𝑦
𝑟
=-ve
Tanβ=
𝑃
𝐵
=
−𝑦
−𝑥
=+ve
Cosecβ=
𝐻
𝑃
=
𝑟
−𝑦
=
Secβ=
𝐻
𝐵
=
𝑟
−𝑥
=-ve
Cotβ=
𝐵
𝑃
=
−𝑥
−𝑦
=+ve
Perpendicular(
P)=-y
Hypotenuse(H)
=r
Base(B) =-x
The ratios of and are positive in third quadrant

21. THANK YOU