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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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TRIGONOMETRIC FUNCTIONSBASIC IDEAS

BY

SIBY SEBASTIAN PGT(MATHS)

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Basic Terms

A

C

B

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Angle Measures and Types of Angles

Types of angles named on basis of measure:

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Measuring Angles

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a)60

b) 221.7

221.70 =

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a)

= x =

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Equivalent Angles in Degrees and Radians

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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

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Trigonometric Functions

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Exponential Notation and

Trigonometric Functions

• sin2 A = (sin A)2

• tan3A = (tanA)3

• Sec5A = (secA)5

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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?

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Mnemonic Techniques

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Domain and Range of Sine Function

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GRAPH OF sine FUNCTION

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Domain and Range of Cosine Function

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GRAPH OF cosine FUNCTION

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Domain and Range of Tangent Function

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GRAPH OF tangent FUNCTION

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Domain and Range of Cosecant Function

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GRAPH OF cosecant FUNCTION

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Domain and Range of Secant Function

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GRAPH OF secant FUNCTION

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Domain and Range of Cotangent Function

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GRAPH OF cotangent FUNCTION

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Ranges of Trigonometric Functions

For any angle  for which the indicated functions exist:

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

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Periodic Properties

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Theorem Even-Odd Properties

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

1.sin(

2.cos() = sinx

3.tan( = cotx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

4.sin(

5.cos() = - sinx

6.tan( = - cotx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

7.sin(

8.cos() = -cosx

9.tan(= - tanx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

10.sin(

11.cos() = -cosx

12.tan( = tanx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

13.sin(

14.cos() = -sinx

15.tan( = cotx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

16. sin(

17 .cos() = sinx

18 .tan( = - cotx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

19.sin(

20.cos() = cosx

21.tan(2 =-tanx

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

• sin2x +cos2x =1

• 1+tan2x =sec2x

• 1+cot2x =cosec2x

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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

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

5.tan(x + y) =

6.tan(x – y) =

7.cot(x + y) =

8.cot(x - y) =

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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)

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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(

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

MULTIPLE ANGLES

1.sin2x = 2sinxcosx =

2.cos2x = cos2x – sin2x = 2cos2x – 1

= 1 – 2sin2x =

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

3.tan2x =

4.sin3x = 3sinx – 4sin3x

5.cos3x = 4cos3x – 3cosx

6.tan3x =

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

SUB MULTIPLE ANGLES

1.sinx = 2sin

2.cosx =

3.1- cosx = 2

4.1+cosx = 2

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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

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

4.Sinx = sinythen,x = n

5.cosx =cosy then

6.tanx = tany then x= n

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

Sine Rule

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BASIC RULES OF TRIGONOMETRIC FUNCTIONS

Cosine Rule

cosA =

cosB =

cosC =

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Finally let us dance together and

enjoy trigonometry

Practice

Practice

&

Practice

Until you get it. ……..

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