The word trigonometry is derived

from Greek words ‘tri’ (meaning

three), ‘gon’ (meaning sides) and

metron (meaning measure). In

fact , The earliest known work on

trigonometry was recorded in Egypt

and Babylon. Early astronomers

used to find out the distance of the

stars and planet s from the Earth.

Introduction

Introduction To Trigonometry

There is no perhaps nothing which so occupies the middle position of mathematics as trigonometry.

-J.F. Herbart(1890)

•Suppose the students of a

school are

visiting Qutub Minar. N

ow, if a student

is looking at the to

p of the Minar a

right tr

iangle could be imagined to

be

made.

• Suppose a girl sitti

ng on the

balcony of her h

ouse located on

the bank of a riv

er. She is looking

down at a flower p

ot placed on

stair of a

temple situ

ated nearby

on the other b

ank of the riv

er. A

right tr

iangle is imagined to

be

made in th

is situatio

n.

Trigonometric ratios

The trigonometric ratios of the angle A in the right triangle ABC see in fig.

•Sin of A =side opposite to angle A =BC

hypotenuse AC

•Cosine of A =side adjacent to angle A =AB

hypotenuse AC

•Tangent of A =side opposite to angle A =BC

side adjacent to angle A ABC

A B

Cosecant of A = 1 = hypotenuse = AC

sin of A side opposite to angle A BC

Secant of A = 1 = hypotenuse = AC

sin of A side adjacent to angle a AB

Cotangent of A= 1 =side adjacent to angle A= AB

tangent of A side opposite to angle A BC

C

A B

These are some easy method to learn these formulas:

•Pandit Badri Prasad Har Har Bhole Sona Chandi

Tole

•Pakistan Bhuka Pyasa Hindustan Hara Bhara.

S C

T

P B

P

H H

B

The first use of the idea of ‘sine’ in the way we use it today was in the work ‘Aryabhatiyam’ by Aryabhatta, in A.D. 500. Aryabhatta used the word ardha-jiva for the half-chord, which shortened to jya or jiva. When it was translated into Latin, the word jiva was translated into sinus, which means curve.

Sin

Sin

Sin

SinSin

Sin

Sin

Sin

Sin

Sin

Sin

Sin

Sin

SinSin

Sin

ORIGIN OF ‘SINE’

Foundation of COSINE & TANGENT

The origin of terms cosinecosine and tangenttangent was much later. The cosine function arose from the need to compute the sine of the complementary angle. AryabhataAryabhata called it kotijyakotijya. The name cosinus originated with Edmund GunterEdmund Gunter. In 1674, the English mathematician Sir Jonas MooreSir Jonas Moore first use the abbreviated notation coscos.

TRIGONOMETRIC RATIOS OF SOME SPECIFIC ANGLES

Trigonometric ratios of some specific angles

Trigonometry ratios of complimentary angles

Recall two angles are said to be complimentary if their sum equals 90°.Sin ( 90° - A) = cos A,

Tan (90°- A ) = cot A,

Sec (90° - A ) = cosec A,

Cos ( 90° - A ) = sin A,

Cot (90° - A) = tan A,

Cosec (90° - A ) = sec A.

WHAT ARE TRIGONOMETRIC IDENTITIES

????An equation involving

trigonometric ratios of an angle is called a Trigonometric

Identitity, if it is true for all values of the angle(s) involved.

Trigonometric identities are ratios and relationships between certain trigonometric functions.

Trigonometric Trigonometric identitiesidentities

• cos²A + sin²A = 1cos²A + sin²A = 1

• 1 + tan²A = sec²A (1 + tan²A = sec²A (0*≤ A ≤ 90*)0*≤ A ≤ 90*)

• cot²A + 1 = cosec²A (cot²A + 1 = cosec²A (0* < A ≤ 0* < A ≤ 90*)90*)

OTHER USEFUL IDENTITIES

• Sin θ = 1/cosec θ• Cos θ = 1/sec θ• Tan θ = 1/cot θ• Cosec θ = 1/sin θ• Sec θ = 1/cos θ• Tan θ = 1/cot θ

The line of sight is the line drawn from the eye of an observer to the point in the object viewed by the observer.

Line of sight

ANGLE OF ELEVATIONWhen a person looks at something above his or her

location, the angle between the line of sight and the horizontal is called the angle of elevation. In this case, the line of sight

is “elevated” above the horizontal.

ANGLE OF DEPRESSIONWhen a person looks at something below his or her

location, the angle between the line of sight and the horizontal is called the angle of depression. In this case, the line of

sight is “depressed” below the horizontal.