TRIGONOMETRY..

YELLOW HOUSE CLASS “10 B”

MEMBERS : DEWAMSH BASYAL RITUSHA KHADKA NISHAN POUDEL

AMIC RAIRIVIKA LAMSAL

NIKITA THAPA

Submitted by:MATHS DEPARTMENT

Submitted to:

Collaboration with: Janak Singh Saud Math's teacher

PRESENTED BY:

DEWAMSHA BASHYAL AND

RITUSHA KHADKA

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

LETS KNOW……• WHAT IS TRIGONOMETRY?

Trigonometry is the branch of mathematics which deals with the measurement of sides and angle of a triangle.

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).

Sin / Cosec

P (pashu

pati ko)H

(halli)

Cos / Sec

B (badha

r)

H (halli)

Tan / Cot

P (pashupatima

)B

(basxa)

This is pretty easy!

BASE (B)

HYPOTENUSE

(H)

PERP

END

ICU

LAR

(P)

Trigonometric ratios...

TRIGONOMETRIC VALUES OF SOME ANGLES...

A 0 30 45 60 90

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

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

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?

APPLICATION…

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

USE OF CLINOMETER• CLINOMETERS IS A DEVICE WHICH IS

USED TO MEASURE THE ANGLE OF ELEVATION AND DEPRESSION WHICH HELPS TO FIND THE HEIGHT OR DISTANCE OF DIFFERENT OBJECTS.

OTHER APPLICATIONS OF TRIGONOMETRY...

ACOUSTICS,SPORTS, ARCHITECTURE, ASTRONOMY, CARTOGRAPHY, CIVIL ENGINEERING, GEOPHYSICS, CRYSTALLOGRAPHY, ELECTRICAL ENGINEERING,ELECTRONICS,PROBABILITY THEORY, 

MECHANICAL ENGINEERING, MACHINING, MEDICAL IMAGING,NUMBER THEORY, OCEANOGRAPHY, OPTICS, SEISMOLOGY, STATISTICS,  VISUAL PERCEPTION LAND SURVEYING AND GEODESY,  PHYSICAL SCIENCES, PHARMACOLOGY, 

HOW TRIGONOMETRY IS USED IN SPORTS.

Basketball

Golf

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.

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.

TRIGONOMETRIC RATIOS...When β=90°

βX

A

C

Y

OX’

Y’

B

IN THIS FIGURE,WHEN OB REACHES OC β=90°BA = OC/OBOA BECOMES OSO,IN OABHYPOTENUSE(OB)=1(LET)BASE(OA) = 0PERPENDICULAR(BA) = 1

THE VALUES OF THE TRIGONOMETRIC RATIOS ARE...

Sinβ= = =1

Cotβ= = =0

Secβ= = = ∞

Cosecβ= ==1

Cosβ= = =0

Tanβ= = =∞

CAST RULE...

C

S

T

ASIN

COSEC COS

SECTANCOT

ALL

THIRD QUADRANT...

X

Y

X’

Y’

-yr

-x

Cosβ= = =-veSinβ= = =-ve

Tanβ= = =+veCosecβ= = =-ve

Secβ= = =-ve

Cotβ= = =+ve

Perpendicular(P)=-yHypotenuse(H)=rBase(B) =-x

The ratios of Tan and Cot are positive in third quadrant

THANK YOU