Trigonometry

INTRODUCTION INTRODUCTION TO TO

TRIGONOMETRYTRIGONOMETRYMADE BY:-

ANISH HAKHU

IX - A

What is Trigonometry?What is Trigonometry?

Trigonometry is the study of how the Trigonometry is the study of how the sides and angles of a triangle are related sides and angles of a triangle are related to each other. to each other.

It's all about triangles!It's all about triangles!

A

Right Triangle

Opposite

Hypotenuse

Adjacent

Same Right Triangle – Different Angle

Hypotenuse

B

Adjacent

Opposite

Trigonometric RatiosTrigonometric Ratios The trigonometric ratios of the angle A in right triangle are The trigonometric ratios of the angle A in right triangle are

defined as follows :defined as follows : Sine of Sine of LLA = A = side opposite to angle Aside opposite to angle A = = BCBC hypotenuse AChypotenuse AC Cosine of Cosine of LLA = A = side adjacent to angle Aside adjacent to angle A = = ABAB hypotenuse AChypotenuse AC Tangent of Tangent of LLA = A = side opposite to angle Aside opposite to angle A = = BCBC side adjacent to angle A ABside adjacent to angle A AB Cosecant of Cosecant of LLA = A = 1 1 = = hypotenuse hypotenuse = = ACAC sine of sine of LLA side opposite to angle A BCA side opposite to angle A BC Secant of Secant of LLA = A = 1 1 = = hypotenuse hypotenuse = = ACAC cosine of cosine of LLA side adjacent to angle A BCA side adjacent to angle A BC Cotangent of Cotangent of LLA = A = 1 1 = = hypotenuse hypotenuse

= = ACAC tangent of tangent of LLA side opposite to angle A A side opposite to angle A

BC BC

A Way To RememberA Way To Remember

SSin = in = OOpposite/pposite/HHypotenuseypotenuse

Oprah Had Oprah Had CCos = os = AAdjacent/djacent/HHypotenuseypotenuse

A HugeA Huge TTan = an = OOpposite/pposite/AAdjacentdjacent

Old Afro Old Afro

y

x

y

x

r

O

x,y

r = x + y2 2 2

Definitions of Trig Definitions of Trig FunctionsFunctions

SinSin == y / ry / r Cos Cos == x / rx / r Tan Tan == y / xy / x CscCsc == r / yr / y SecSec == r / xr / x CotCot = = x / yx / y

O

O

O

OOO

Radius = 1

The Unit CircleThe Unit Circle

y

x

1/2

30

x,y

r = x + y2 2 2

1

√3/2

y

x

√/2/2

45

x,y

r = x + y2 2 2

1

√2/2

y

x

1/2

60

x,y

r = x + y2 2 2

1

√3/2

The Unit Circle-Special The Unit Circle-Special Angles Angles

and Their Exact Valuesand Their Exact Values

THE END