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Trigonometry

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... = Tan IDENTITIES IN TRIGNOMETRY 1. Sin2 +Cos2 =1 2. Sec2 -Tan2 =1 3.Cosec2 -Cot2 =1 Some More Formulas If 00 – PowerPoint PPT presentation

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Title: Trigonometry


1
Welcome to
Trigonometry
World
Presented by Nalini Harbhajan
kaur Maths Mistress Pb Mistress G.H.S
G.S.S.S Rohajri
Naugajja
2
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.

3
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.

4
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.

5
PHYTHAGOROUS THEOREM
  • In righted triangle ABC right angled at B.
  • h2 p2 b2
  • Where h hypotenuse
  • pperpendicular
  • bbase

6
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.

7
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.

8
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

9
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

10
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
11
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

12
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

13
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

14
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

15
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

16
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

17
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

18
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

19
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

20
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

21
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

22
Some More Formulae
  • If 00lt T lt900
  • 1.Sin(900- T) Cos T
  • 2.Cos(900- T) Sin T

23
Some More Formulae
  • If 00lt T lt900
  • Tan(900- T) Cot T
  • .If 00lt T lt900
  • Cot(900- T) Tan T

24
IDENTITIES IN TRIGNOMETRY
  • 1. Sin2TCos2T 1
  • 2. Sec2 T -Tan2 T 1
  • 3.Cosec2 T -Cot2 T 1

25
Some More Formulas
  • If 00ltTlt900
  • Sec(900-T) CosecT
  • If 00ltTlt900
  • Cosec(900-T) SecT

26

A LOT OF THANX
DIET PRINCIPAL
and
INSTRUCTOR PARVEEN KUMAR
27
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