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Welcome to

Trigonometry

World

Presented by Nalini Harbhajan

kaur Maths Mistress Pb Mistress G.H.S

G.S.S.S Rohajri

Naugajja

Objectives

- To make the students familiar with term

trigonometry ,uses of it ,basic formulas of it. - 2. To create interest of students in it.
- 3.To make teaching of trigonometry effective.

What is Trigonometry

- It is an important branch of mathematics
- It is drived from to Greek words
- Trigonon meaning a triangle and
- metron meaning measurement.
- Thus the word trigonometry means the science

which deals with the measurement of triangle.

Uses of Trigonometry

- Trigonometry helps us in calculating

remaining sides and angles of right angled

triangle. - Knowledge of trigonometry has been used

extensively in Astronomy , Surveying , Geography

, Navigation , Physical and Engineering Sciences

etc.

PHYTHAGOROUS THEOREM

- In righted triangle ABC right angled at B.
- h2 p2 b2
- Where h hypotenuse
- pperpendicular
- bbase

Explanation about sides of triangle.

- Let T be acute angle in right angled triangle ABC

right angled at B. - 1. AB is opposite side
- to angle T .
- . 2. BC is adjacent side
- to angle T.
- 3 .AC is hypotenuse.

What is T-ratio or Trigonometric ratio.

- Some ratio of different sides of a right triangle

called T-ratio or Trigonometric ratio e.g

.Sine,Cosine.

Sine of an angle.

- The ratio AB\AC is called the Sine of angle T.In

short it is written as Sin T. - Sin T AB/AC
- opposite side/hypotenuse
- p/h

Cosine of an angle.

- The ratio BC/AC is called the cosine of angle T.

In short it is written as Cos T. - Cos T BC/AC
- adjacent side/hypotenuse
- b/h

Tangent of an angle

- The ratio AB/BC is called the tangent of angle

T.In short it is written as Tan T. - Tan T AB/BC
- opposite side/adjacent side
- p/b

bb

RELATION BETWEENSin T Cos T and Tan T

- Sin T p/h..(1)
- Cos T b/h.(2)
- On dividing (1) by (2) We get
- Sin T\ Cos T p/b Tan T
- (As We know Tan T p/b)
- ? Sin T /Cos T Tan T

Cosecant of an angle

- The ratio AC/AB is called Cosecant of an angle

T.In short it is written as Cosec T. - Cosec T hypotenuse/opposite side
- AC/AB
- h/p

Secant of an angle

- The ratio AC/BC is called Secant of angle T.In

short it is written as SecT. - Sec T hypotenuse /adjacent side
- AC/BC
- h / b

Cotangent of an angle

- The ratio BC/AC is called Cotangent of angle T.In

short it is written as Cot T. - Cot T adjacent side/opposite side
- BC/AC
- b / p

Relation among T-ratio

- Tan T Sin T/Cos T
- Cosec T 1/Sin T
- Sec T 1/Cos T
- Cot T Cos T /Sin T
- 1/Tan T

POPULAR SONG TO LEARN

- SARAE CHELAE TERE
- PANDIT BADRI PARSAD
- HAR HAR BOLE
- IN short it is written as
- S C T
- P B P
- H H B

Table

- 1.Sin T p/ h
- 2.Cos T b/ h
- 3.Tan T p/ b
- 4.Cosec T h/ p
- 5.Sec T h/ b
- 6.Cot T b/ p

T RATIO OF SOME SPECIFIC ANGLES

- T 0 0 30 0 450 600

900 Sin T 0 1/2 1/v2

v 3/2 1 - Cos T 1 v 3/2 1/v2 1/2 0
- Tan T 0 1/v3 1 v3

1/0 - Cosec T 1//0 2 v 2 2/v3

1 - Sec T 1 2/v3 v 2 2

1/0 - Cot T 1/0 v 3 1 1/v3

1

Relation of T with Sin Twhen 0 0 lt Tlt 900

- The greater the value of T, the greater is the

value of Sin T. - Smallest value of Sin T 0
- Greatest value of Sin T 1

Relation of T with Cos T when 0 0 lt Tlt 900

- The greater the value of T , the smaller the

value of Cos T. - Smallest value of Cos T 0
- Greatest value of Cos T 1

Relation of T with Tan T When 0 0 ltT lt 900

- Tan T increases as T increases but
- Tan T is not defined (1/0)
- at T 900
- Smallest value of Tan T 0

Some More Formulae

- If 00lt T lt900
- 1.Sin(900- T) Cos T
- 2.Cos(900- T) Sin T

Some More Formulae

- If 00lt T lt900
- Tan(900- T) Cot T
- .If 00lt T lt900
- Cot(900- T) Tan T

IDENTITIES IN TRIGNOMETRY

- 1. Sin2TCos2T 1
- 2. Sec2 T -Tan2 T 1
- 3.Cosec2 T -Cot2 T 1

Some More Formulas

- If 00ltTlt900
- Sec(900-T) CosecT
- If 00ltTlt900
- Cosec(900-T) SecT

A LOT OF THANX

DIET PRINCIPAL

and

INSTRUCTOR PARVEEN KUMAR

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