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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)

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By siby sebastian pgt maths

TRIGONOMETRIC FUNCTIONSBASIC IDEAS

BY

SIBY SEBASTIAN PGT(MATHS)

siby sebastian pgt maths


By siby sebastian pgt maths

Basic Terms

A

C

B

siby sebastian pgt maths


By siby sebastian pgt maths

Angle Measures and Types of Angles

Types of angles named on basis of measure:

siby sebastian pgt maths


By siby sebastian pgt maths

Measuring Angles

siby sebastian pgt maths


By siby sebastian pgt maths

Radian Measure

siby sebastian pgt maths


By siby sebastian pgt maths

Comments on Radian Measure

siby sebastian pgt maths


By siby sebastian pgt maths

Conversion Between Degrees and Radians

siby sebastian pgt maths


By siby sebastian pgt maths

Convert Degrees to Radians

a)60

b) 221.7

221.70 =

siby sebastian pgt maths


By siby sebastian pgt maths

Convert Radians to Degrees

a)

= x =

b) 3.25 rad

3.25 rad = x

siby sebastian pgt maths


By siby sebastian pgt maths

Equivalent Angles in Degrees and Radians

siby sebastian pgt maths


By siby sebastian pgt maths

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


By siby sebastian pgt maths

Trigonometric Functions

siby sebastian pgt maths


By siby sebastian pgt maths

Exponential Notation and

Trigonometric Functions

  • sin2 A = (sin A)2

  • tan3A = (tanA)3

  • Sec5A = (secA)5

siby sebastian pgt maths


By siby sebastian pgt maths

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


By siby sebastian pgt maths

Mnemonic Techniques

siby sebastian pgt maths


By siby sebastian pgt maths

Domain and Range of Sine Function

siby sebastian pgt maths


By siby sebastian pgt maths

GRAPH OF sine FUNCTION

Click here to see how sin function is generated

siby sebastian pgt maths


By siby sebastian pgt maths

Domain and Range of Cosine Function

siby sebastian pgt maths


By siby sebastian pgt maths

GRAPH OF cosine FUNCTION

Click here to see how cosine function is generated

siby sebastian pgt maths


By siby sebastian pgt maths

Domain and Range of Tangent Function

siby sebastian pgt maths


By siby sebastian pgt maths

GRAPH OF tangent FUNCTION

Click here to see how tangent function is generated

siby sebastian pgt maths


By siby sebastian pgt maths

Domain and Range of Cosecant Function

siby sebastian pgt maths


By siby sebastian pgt maths

GRAPH OF cosecant FUNCTION

siby sebastian pgt maths


By siby sebastian pgt maths

Domain and Range of Secant Function

siby sebastian pgt maths


By siby sebastian pgt maths

GRAPH OF secant FUNCTION

siby sebastian pgt maths


By siby sebastian pgt maths

Domain and Range of Cotangent Function

siby sebastian pgt maths


By siby sebastian pgt maths

GRAPH OF cotangent FUNCTION

siby sebastian pgt maths


By siby sebastian pgt maths

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


By siby sebastian pgt maths

Periodic Properties

siby sebastian pgt maths


By siby sebastian pgt maths

Theorem Even-Odd Properties

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

1.sin(

2.cos() = sinx

3.tan( = cotx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

4.sin(

5.cos() = - sinx

6.tan( = - cotx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

7.sin(

8.cos() = -cosx

9.tan(= - tanx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

10.sin(

11.cos() = -cosx

12.tan( = tanx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

13.sin(

14.cos() = -sinx

15.tan( = cotx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

16. sin(

17 .cos() = sinx

18 .tan( = - cotx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

19.sin(

20.cos() = cosx

21.tan(2 =-tanx

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

  • sin2x +cos2x =1

  • 1+tan2x =sec2x

  • 1+cot2x =cosec2x

siby sebastian pgt maths


By siby sebastian pgt maths

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


By siby sebastian pgt maths

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


By siby sebastian pgt maths

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


By siby sebastian pgt maths

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


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

MULTIPLE ANGLES

1.sin2x = 2sinxcosx =

2.cos2x = cos2x – sin2x = 2cos2x – 1

= 1 – 2sin2x =

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

3.tan2x =

4.sin3x = 3sinx – 4sin3x

5.cos3x = 4cos3x – 3cosx

6.tan3x =

siby sebastian pgt maths


By siby sebastian pgt maths

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


By siby sebastian pgt maths

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


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

4.Sinx = sinythen,x = n

5.cosx =cosy then

6.tanx = tany then x= n

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

Sine Rule

siby sebastian pgt maths


By siby sebastian pgt maths

BASIC RULES OF TRIGONOMETRIC FUNCTIONS

Cosine Rule

cosA =

cosB =

cosC =

siby sebastian pgt maths


By siby sebastian pgt maths

Finally let us dance together and

enjoy trigonometry

Practice

Practice

&

Practice

Until you get it. ……..

siby sebastian pgt maths


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