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TRIGONOMETRIC FUNCTIONS BASIC IDEAS. BY SIBY SEBASTIAN PGT(MATHS). Basic Terms. A. C. B. Angle Measures and Types of Angles. Types of angles named on basis of measure:. Measuring Angles. Radian Measure. Comments on Radian Measure. Conversion Between Degrees and Radians.

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by siby sebastian pgt maths

TRIGONOMETRIC FUNCTIONSBASIC IDEAS

BY

SIBY SEBASTIAN PGT(MATHS)

siby sebastian pgt maths

slide2

Basic Terms

A

C

B

siby sebastian pgt maths

slide3

Angle Measures and Types of Angles

Types of angles named on basis of measure:

siby sebastian pgt maths

slide4

Measuring Angles

siby sebastian pgt maths

slide5

Radian Measure

siby sebastian pgt maths

slide6

Comments on Radian Measure

siby sebastian pgt maths

slide8

Convert Degrees to Radians

a) 60

b) 221.7

221.70 =

siby sebastian pgt maths

slide9

Convert Radians to Degrees

a)

= x =

b) 3.25 rad

3.25 rad = x

siby sebastian pgt maths

slide11

Trigonometric Functions

In a circle of radius ‘r’ units and if P(x,y) is a point on the circle then the trigonometric functions are defined by

sincosec

cossec

tancot =

r

y

x

siby sebastian pgt maths

slide12

Trigonometric Functions

siby sebastian pgt maths

slide13

Exponential Notation and

Trigonometric Functions

  • sin2 A = (sin A)2
  • tan3A = (tanA)3
  • Sec5A = (secA)5

siby sebastian pgt maths

slide14

Signs of Trig Functions by Quadrant of Angle

  • Considering the following three functions and the sign of x, y and r in each quadrant, which functions are positive in each quadrant?

siby sebastian pgt maths

slide15

Mnemonic Techniques

siby sebastian pgt maths

slide16

Domain and Range of Sine Function

siby sebastian pgt maths

slide17

GRAPH OF sine FUNCTION

Click here to see how sin function is generated

siby sebastian pgt maths

slide18

Domain and Range of Cosine Function

siby sebastian pgt maths

slide19

GRAPH OF cosine FUNCTION

Click here to see how cosine function is generated

siby sebastian pgt maths

slide20

Domain and Range of Tangent Function

siby sebastian pgt maths

slide21

GRAPH OF tangent FUNCTION

Click here to see how tangent function is generated

siby sebastian pgt maths

slide23

GRAPH OF cosecant FUNCTION

siby sebastian pgt maths

slide24

Domain and Range of Secant Function

siby sebastian pgt maths

slide25

GRAPH OF secant FUNCTION

siby sebastian pgt maths

slide27

GRAPH OF cotangent FUNCTION

siby sebastian pgt maths

slide28

Ranges of Trigonometric Functions

For any angle  for which the indicated functions exist:

Note that sec  and csc are never between 1 and 1

siby sebastian pgt maths

slide29

Periodic Properties

siby sebastian pgt maths

slide30

Theorem Even-Odd Properties

siby sebastian pgt maths

slide31

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

1.sin(

2.cos() = sinx

3.tan( = cotx

siby sebastian pgt maths

slide32

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

4.sin(

5.cos() = - sinx

6.tan( = - cotx

siby sebastian pgt maths

slide33

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

7.sin(

8.cos() = -cosx

9.tan(= - tanx

siby sebastian pgt maths

slide34

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

10.sin(

11.cos() = -cosx

12.tan( = tanx

siby sebastian pgt maths

slide35

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

13.sin(

14.cos() = -sinx

15.tan( = cotx

siby sebastian pgt maths

slide36

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

16. sin(

17 .cos() = sinx

18 .tan( = - cotx

siby sebastian pgt maths

slide37

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

19.sin(

20.cos() = cosx

21.tan(2 =-tanx

siby sebastian pgt maths

slide38

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

  • sin2x +cos2x =1
  • 1+tan2x =sec2x
  • 1+cot2x =cosec2x

siby sebastian pgt maths

slide39

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

SUM AND DIFFERENCE OF TWO ANGLES

1.cos(x + y) = cosxcosy – sinxsiny

2.cos(x – y) = cosxcosy + sinxsiny

3.sin(x + y) = sinxcosy + cosxsiny

4.sin( x – y) = sinxcosy - cosxsiny

siby sebastian pgt maths

slide40

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

5.tan(x + y) =

6.tan(x – y) =

7.cot(x + y) =

8.cot(x - y) =

siby sebastian pgt maths

slide41

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

PRODUCT AS SUM OR DIFFERENCE

1 .2sinxcosy = sin(x + y) + sin(x – y)

2. 2cosxsiny = sin(x + y) – sin(x – y)

3.2cosxcosy = cos(x + y)+cos(x – y)

4.-2sinxsiny = cos(x + y) – cos(x – y)

siby sebastian pgt maths

slide42

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

SUM OR DIFFERENCE AS PRODUCT

1.sinx + siny = 2sin(

2.sinx – siny = 2cos(

3.cosx + cosy = 2cos(

4.cosx – cosy = - 2sin(

siby sebastian pgt maths

slide43

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

MULTIPLE ANGLES

1.sin2x = 2sinxcosx =

2.cos2x = cos2x – sin2x = 2cos2x – 1

= 1 – 2sin2x =

siby sebastian pgt maths

slide44

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

3.tan2x =

4.sin3x = 3sinx – 4sin3x

5.cos3x = 4cos3x – 3cosx

6.tan3x =

siby sebastian pgt maths

slide45

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

SUB MULTIPLE ANGLES

1.sinx = 2sin

2.cosx =

3.1- cosx = 2

4.1+cosx = 2

siby sebastian pgt maths

slide46

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

GENERAL SOLUTIONS

1.sinx =0 then x= n, n

2.cosx = 0 then x=(2n + 1) n

3.tanx =0 then x= n, n

siby sebastian pgt maths

slide47

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

4.Sinx = sinythen,x = n

5.cosx =cosy then

6.tanx = tany then x= n

siby sebastian pgt maths

slide48

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

Sine Rule

siby sebastian pgt maths

slide49

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

Cosine Rule

cosA =

cosB =

cosC =

siby sebastian pgt maths

slide50

Finally let us dance together and

enjoy trigonometry

Practice

Practice

&

Practice

Until you get it. ……..

siby sebastian pgt maths

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