Trigonometry for JEE (Advanced), 3rd edition 9353503809, 9789353503802

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Contents

Trigonometric

Functions

of an

2.9

Angle

2.9

Angles in Trigonometry Preface

1.1-1.27

lts Properties Logarithm and Exponential Function Function and Its

Graph of Exponential Function for Graph of Exponential

Properties

Different Bases

Function

Change of Base

wherefr) is Exponential

Function

Logarithmnic Equations

Logarithmnic Inequalities Standard Logarithmic Inequalities Finding Logarithm

Characteristic and Mantissa of Logarithm Mantissa Using Log Table

Finding

Negative Characteristics

Antilogarithm To Find Antilog of a

Number

Solved Examples Exercises

Single Corect Answer Type Multiple Correct Answers Type

Linked Comprehension Type Matrix Match Type Numerical Value Type

2.

2.1-2.32 2.1

Trigonometric Ratios of Standard Angles

2.1

Trigonometric Identities Measurement of Angle Degree Measurement Radian Measurement Conversion between Radians and Degrees Relation between Radians and Real Numbers

2.4 2.7 2.7 2.7 2.7 2.7

2.12 2.13 2.19

2.19

x

90°

6 when n

2.20

is Odd

2.23 .26

Exercises

2.26 2.28

Type Single Correct Answers TypDe Correct Multiple Linked Comprehension Type Matrix Match Type Answer

2.29

2.30 2.30

Numerical Value Type

2.31 2.31

Archives

1.16 1.16

1.27

Circular

Solved Examples

1.12

Answers Key Trigonometric F unctions Trigonometric Ratios/Functions of Acute Angles

n

1.12

1.27

as

Trigonometric

1.11

Archives

Functions Defined

Graph

1.7 1.8 1.9 1.9

1.25 .26 1.26

2.12

Functions

of Alied Angles Trigonometric Ratios of Allied Angles Trigonometric Ratios + 0 when n is Even n x 90° Ratios of Allied Angles

1.6 1.6

1.18 1.18 1.20 1.23 1.23 1.25

2.11

of Any Angle

Functions Functions of Trigonometric

1.2

1.16 1.17

Functions

of Trigonometric

Trigonometric

1.4

Reciprocal of Logarithm )

Behaviour

for Different

Bases Fundamental Laws of Logarithm of Logarithm Addition and Subtraction and Base of Logarithm of Argument Exponents

Sf

1.1 1.1 1.3 1.3

Logarithmic Function

Graph of the Logarithmic Function Graph of the Logarithmic

Trigonometric

Answers Key

3.

Trigonometric Ratios and

Transformation

3.1-3.48

Formulas and Sine

Compound Angle Formulas for Cosine Cosine of the Difference and Sum of the Angles Sine of the Difference and Sum of The Angles Some More Results

Expression

a

cos x

+b sin

x

3.1

3.1 3.1 3.1 3.4

Compound Angle Formulas for Tangent

3.6

Transformation Formula Formula to Transform the Product into Sum or

3.8

3.8

Difference

Formulas to Transform the Sum or Difference into Product Trigonometric Ratios of Multiple Angles Formulas for Sine and Cosine of Multiple Formulas for Tangent and Cotangent of Multiple

Angles

Angles

3.8 3.11 3.11

3.16

Values of Trigonometric Ratios of Typical Angles

3.18

Some Important Results and Their Applications

3.21

Sum of Cosines and Sines when Angles are in A.P,

3.23

Conditional Identities

3.24

iv Content Some Standard Identities in Triangle

3.24

Finding Range of Expression Using Trigonometric Substitution Inequalities in Triangle Some Standard Inequalities in Triangle

3.27 3.28

3.28

Solved Examples

3.31

Exercises

3.36

Single Correct Answer Type

Multiple Correct Answers Type Matrix Match Tvpe

Three Angles (AAA)

5.16

Properties of Circumcircle and Length of Tangent

Distance of Incentre from the Vertices of Triangle

Bisector Orthocentre and Centroid

Distance of Orthocentre from Vertices and Sides Pedal Triangle and Orthic Triangle Centroid of Triangle Escribed Circle and Excentre Radii of Excircles (Exradii) Distance between Incentre and Excentre Distance between Excentres

4.1

Important Points in Solving Trigonometrie 4.3 4.4 4.6 4.8

Trigonometric Equation (f&) = (S(0,

where f ) is Trigonometric Function

Regular Polygon

4.10

Trigonometric Equation a cos x +b sin x = c

Radii of the Inscribed and the Circumscribed Circles of a Regular Polygon

4.11

Solving Trigonometric Equations Using Maximum/

5.19

5.20

Length

4.1-4.31

5.19 5.19

5.19

3.47

Iigonometric Equation tan x = tan a

5.17

Different Formulas for Inradius

Answers Ker

Trigonometric Equation cos x = cos o

5.11

from Vertices to the Incircle

3.46

Trigonometric Equation sin x == sin a.

5.15

Incircle and Incentre

of Angle Bisector Division of Opposite Side by the Internal Angle

Equations

5.15

Circumcentre

Numerical V'alue Type Archives

Trigonometric Equations Trigonometric Equations

Area of Regular Polygon

5.25 5.25 5. 26

5 27

5.29

5.29 5.31 5.31 5.32 5.32 5.32

Minimum Value of Function

4.13

Solving Equations Using Graphs Trigonometric Inequalities

Solved Examples

5.34

4.14

Exercises

5.40

Soved Examples Exercises Single Correct Answer Type

Multiple Correct Answers Type Linked Comprehension Type Matrix Match Type Numerical Value Type

Single Correct Answer Type Multiple Correct Answers Type

4.17 4.21 4.21 4.25 4.27

Numerical Value Type Archives

4.28

Answers Key

4.29

Answers Key

5.40 5. 5.

Linked Comprehension Type Matrix Match Type

6.

4.31

Properties and Solutions of Triangle

Introduction.

5.47 5.48 5.49

5.51

5.1-5.51 5.1 5.4 5.5

Napier Formula (tan rule) m-n Theorem

Cosine Rule

5.6

Projection Rule

5.9

Half Angle Formulas

Half Angle Formulas for Sine Half Angle Formulas for Cosine Area of Triangle Area of Quadrilateral

5.9 5.9 5.10 5.11 5.14

Solutions of Triangle Three Sides (SSS)

Angle (SAS)

5.14 5.15 5.15

Height and Distance Introduction

6.1-6.1 6.1 6.1

Solved Examples Exercises Single Correct Answer Type Archives Answers Key

5.1

Sine Rule

Two Sides and the Included

4.16

4.29

Archives

5.

5.15

Circumcircle and Circumcentre

3.36 3.41 3.42 3.43 3.44

Linked Comprehensiom Type

A Side and the Two Angles Adjacent to It (ASA) A Side, the Angle Opposite to It and an Angle Adjacent to It (AAS) Two Sides and an Angle not Included between Them (SSA)

6. 6.4 6. 6..

7.

Inverse

Trigonometric Functions

7.1-7.43

Introduction

7.

Inverse Trigonometric Functions

Graph of Inverse Trigonometric Function

Function f(S), where f(r) is Function

1.2

Trigonometric

Principal Values of Principal Value ofFunctionf(f(x) sin (sin x)

Principal Value of cos (cos x) Principal Value of tan (tan x)

7.

7.7

7.9 7.10

Content

7.10

of (cot x) Principal Value cot (cosec x) of Principal Value cosec Value of sec" (sec x)

Principal

7.10

7.10

Inverse Trigonometric Functions

Relating Different Trigonometric Simplifying Expression Using

Substitution Relating() withf -t)

Relatingfx) with f"(1/1) Complementary Angles otf Angles in Terms of tan Sum and Difference of Angles in Terms ofsin Sum and Difference

and cos

Multiple Angles in Ternms of sin

Sohved Examples

'r and cos

7.11 7.12

S.1-S.157

S.1

Chapter 1

7.16

Chapter 4

7.19

Chapter 5

7.24 7.26 7.29

Matrir Match Type

7.40

Mulriple Correct Answers Type

7.43

Solutions Chapter 2

Linked Comprehension Type

Single Corect Answer Type

7.41

Archives Answers Key

7.13 7.14

7.33 7.33 7.37 7.39

Exercises

7.40

Numerical Value Type

S.17

S.32

Chapter 3

S.66

S.93 S.127

Chapter 6

x

V

S.131

Chapter 7 Appendix 1:

Logarithm and Antilogarithm

Tables

A.1-A.6

Appendix 2:

Chapterwise Solved January Questions (All Sets)

2019 JEE Main

A.7-A.8