# Learning Mathematics for IIT JEE

## Friday, February 27, 2015

## Wednesday, December 24, 2014

### 33. Trigonometric ratios, Identities and Maximum & Minimum Values of Trigonometrical Expressions - Revision Facilitator

Sections in the chapter

33.1 Introduction

33.2 Some basic formulae

33.3 Domain and range of trigonometrical functions

33.4 Sum and difference formulae

33.5 Sum and difference into products

33.6 Product into sum or difference

33.7 T-ratios of the sum of three or more angles

33.8 Values of trigonometrical ratios some important angles and some important results.

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.

33.10 Maximum and minimum values of trigonometrical functions

Study Plan

Day 1

33.1 to 33.4

33.1 Introduction

33.2 Some basic formulae

33.3 Doman and range of trigonometrical functions

33.4 Sum and difference formulae

Do objective type exercises 58,

Day 2

33.5 Sun and difference into products

33.6 product into sum and difference

Do objective type exercises 84,91, 92, 104, 115,

Day 3

33.7 T-ratios of the sum of three or more angles

Do objective type exercises 39, 44, 106, 113, 117,

Day 4

33.8 Values of trigonometric ratios of some important angles and some important results

Do objective type exercises 1,2,3,5,6,7,8,9,10,11

Day 5

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A

Do objective type exercises 12,13,14,15,16,17,19,20,21,22

Day 6

33.10 maximum and minimum values of trigonometrical functions

O.T.E.: 4,18,23-30

Day 7

O.T.E.: 31 to 50

Day 8

O.T.E.: 51 to 70

Day 9

O.T.E.: 71 to 90

Day 10

O.T.E.: 91 to 110

Revision Period

Day 11

O.T.E.: 111 to 120

Day 12

O.T.E.: 121 to 130

Day 13

O.T.E.: 131 to 140

Day 14

O.T.E.: 141 to 148

Day 15

Fill in the blanks type exercise: 1 to 10

Day 16

Fill in the blanks type exercise: 11 to 20

Day 17

Fill in the blanks type exercise: 21 to 30

Day 18

Fill in the blanks type exercise: 31 to 36

Day 19

True/false type exercise: 1 to 12

Day 20

Fill in the blanks type exercise: 13 to 25

Day 21

Practice Exercise: 1 to 10

Day 22

Practice Exercise: 11 to 20

Day 23

Practice Exercise: 21 to 32

Day 24

Formula Revision

Day 25

Formula Revision

33.1 Introduction

33.2 Some basic formulae

33.3 Domain and range of trigonometrical functions

33.4 Sum and difference formulae

33.5 Sum and difference into products

33.6 Product into sum or difference

33.7 T-ratios of the sum of three or more angles

33.8 Values of trigonometrical ratios some important angles and some important results.

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.

33.10 Maximum and minimum values of trigonometrical functions

33.1 Introduction

33.2 Some basic formulae

33.3 Domain and range of trigonometrical functions

33.4 Sum and difference formulae

33.5 Sum and difference into products

33.6 Product into sum or difference

33.7 T-ratios of the sum of three or more angles

33.8 Values of trigonometrical ratios some important angles and some important results.

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.

33.10 Maximum and minimum values of trigonometrical functions

Study Plan

Day 1

33.1 to 33.4

33.1 Introduction

33.2 Some basic formulae

33.3 Doman and range of trigonometrical functions

33.4 Sum and difference formulae

Do objective type exercises 58,

Day 2

33.5 Sun and difference into products

33.6 product into sum and difference

Do objective type exercises 84,91, 92, 104, 115,

Day 3

33.7 T-ratios of the sum of three or more angles

Do objective type exercises 39, 44, 106, 113, 117,

Day 4

33.8 Values of trigonometric ratios of some important angles and some important results

Do objective type exercises 1,2,3,5,6,7,8,9,10,11

Day 5

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A

Do objective type exercises 12,13,14,15,16,17,19,20,21,22

Day 6

33.10 maximum and minimum values of trigonometrical functions

O.T.E.: 4,18,23-30

Day 7

O.T.E.: 31 to 50

Day 8

O.T.E.: 51 to 70

Day 9

O.T.E.: 71 to 90

Day 10

O.T.E.: 91 to 110

Revision Period

Day 11

O.T.E.: 111 to 120

Day 12

O.T.E.: 121 to 130

Day 13

O.T.E.: 131 to 140

Day 14

O.T.E.: 141 to 148

Day 15

Fill in the blanks type exercise: 1 to 10

Day 16

Fill in the blanks type exercise: 11 to 20

Day 17

Fill in the blanks type exercise: 21 to 30

Day 18

Fill in the blanks type exercise: 31 to 36

Day 19

True/false type exercise: 1 to 12

Day 20

Fill in the blanks type exercise: 13 to 25

Day 21

Practice Exercise: 1 to 10

Day 22

Practice Exercise: 11 to 20

Day 23

Practice Exercise: 21 to 32

Day 24

Formula Revision

Day 25

Formula Revision

**Revision facilitator**33.1 Introduction

33.2 Some basic formulae

33.3 Domain and range of trigonometrical functions

33.4 Sum and difference formulae

33.5 Sum and difference into products

33.6 Product into sum or difference

33.7 T-ratios of the sum of three or more angles

33.8 Values of trigonometrical ratios some important angles and some important results.

33.9 Expressions of sin A/2 and cos A/2 in terms of sin A.

33.10 Maximum and minimum values of trigonometrical functions

### IIT JEE Mathematics Study Guide Ch.34 Properties of Triangles and circles connected with them - Revision Facilitator

Recollect and see how many things do you remember

34.1 Introduction

34.2 Sine rule

34.3 Cosine formulae

344 Projection formulae

34.5 Trigonometrical ratios of half of the angles of a triangle

34.6 Area of a triangle

34.7 Napier’s analogy

34.8 Circumcircle of a triangle

34.9 Inscribed circle or incircle of a triangle

34.10 Escribed circles of a triangle

34.11 Orthocentre and its distances from the angular points of a triangle

34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon

34.13 Area of a cyclic quadrilateral

34.14 Ptolemy’s theorem

34.15 Circum-radius of a cyclic quadrilateral

Study Plan

Day 1

Study sections 34.1 to 34.5

34.1 Introduction

34.2 Sine rule

34.3 Cosine formulae

34.4 Projection formulae

34.5 Trigonometrical ratios of half of the angles of a triangle

Day 2

Study Sections 34.6, 34.7, 34.8, 34.9,

34.6 Area of a triangle

34.7 Napier’s analogy

34.8 Circumcircle of a triangle

34.9 Inscribed circle or incircle of a triangle

Attempt Objective Type Exercises 1 to 10

Day 3

34.10, 34.11

34.10 Escribed circles of a triangle

34.11 Orthocentre and its distances from the angular points of a triangle

Attempt objective type exercises 11 to 20

Day 4

Study 34.12 to 34.15

34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon

34.13 Area of a cyclic quadrilateral

34.14 Ptolemy’s theorem

34.15 Circum-radius of a cyclic quadrilateral

Attempt obj type exercises 21 to 30.

Day 5

Attempt obj type exercises 31 to 45.

Day 6

Attempt obj type exercises 46 to 60.

Day 7

Attempt obj type exercises 61 to 75.

Day 8

Attempt obj type exercises 76 to 90.

Day 9

Attempt fill in the blanks 1 to 15.

Day 10

Attempt fill in the blanks 16 to 31.

Day 11

Practice Exercise 1 to 21

Days 12 to 20

Revision

34.1 Introduction

34.2 Sine rule

34.3 Cosine formulae

344 Projection formulae

34.5 Trigonometrical ratios of half of the angles of a triangle

34.6 Area of a triangle

34.7 Napier’s analogy

34.8 Circumcircle of a triangle

34.9 Inscribed circle or incircle of a triangle

34.10 Escribed circles of a triangle

34.11 Orthocentre and its distances from the angular points of a triangle

34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon

34.13 Area of a cyclic quadrilateral

34.14 Ptolemy’s theorem

34.15 Circum-radius of a cyclic quadrilateral

Study Plan

Day 1

Study sections 34.1 to 34.5

34.1 Introduction

34.2 Sine rule

34.3 Cosine formulae

34.4 Projection formulae

34.5 Trigonometrical ratios of half of the angles of a triangle

Day 2

Study Sections 34.6, 34.7, 34.8, 34.9,

34.6 Area of a triangle

34.7 Napier’s analogy

34.8 Circumcircle of a triangle

34.9 Inscribed circle or incircle of a triangle

Attempt Objective Type Exercises 1 to 10

Day 3

34.10, 34.11

34.10 Escribed circles of a triangle

34.11 Orthocentre and its distances from the angular points of a triangle

Attempt objective type exercises 11 to 20

Day 4

Study 34.12 to 34.15

34.12 Regular polygons and radii of the inscribed and circumscribing circles of a regular polygon

34.13 Area of a cyclic quadrilateral

34.14 Ptolemy’s theorem

34.15 Circum-radius of a cyclic quadrilateral

Attempt obj type exercises 21 to 30.

Day 5

Attempt obj type exercises 31 to 45.

Day 6

Attempt obj type exercises 46 to 60.

Day 7

Attempt obj type exercises 61 to 75.

Day 8

Attempt obj type exercises 76 to 90.

Day 9

Attempt fill in the blanks 1 to 15.

Day 10

Attempt fill in the blanks 16 to 31.

Day 11

Practice Exercise 1 to 21

Days 12 to 20

Revision

### IIT JEE Mathematics Study Guide Ch. 35. Trigonometrical equations and Revision Facilitator

Sections in the chapter R D Sharma

35.1 Trigonometrical equations

Study Plan

Day 1

35.1 Trigonometrical equations

Objective Type Exercise: 1 to 20

Day 2

O.T.E.: 21 to 40

Day 3

O.T.E.: 41 to 60

Day 4

O.T.E.: 61 to 73

Day 5

Fill in the blanks type exercise 1 to 16

Try to recollect relevant points on the topic and if required right click on the topic if link is given and open in a new window to read the relevant material. Close the window and come back.

35.1 Trigonometrical equations

Periodic Function

Period of a Function

General solutions of simple trigonometric equations

Join Orkut Community for more interaction

IIT JEE Academy

http://www.orkut.co.in/Main#Community.aspx?cmm=39291603

35.1 Trigonometrical equations

Study Plan

Day 1

35.1 Trigonometrical equations

Objective Type Exercise: 1 to 20

Day 2

O.T.E.: 21 to 40

Day 3

O.T.E.: 41 to 60

Day 4

O.T.E.: 61 to 73

Day 5

Fill in the blanks type exercise 1 to 16

Try to recollect relevant points on the topic and if required right click on the topic if link is given and open in a new window to read the relevant material. Close the window and come back.

35.1 Trigonometrical equations

Periodic Function

Period of a Function

General solutions of simple trigonometric equations

Join Orkut Community for more interaction

IIT JEE Academy

http://www.orkut.co.in/Main#Community.aspx?cmm=39291603

### IIT JEE Mathematics Study Guide 36. Inverse Trigonometrical functions and Revision Facilitator

Sections in the Chapter R D Sharma

36.1 Inverse Trigonometrical functions

36.2 Properties of inverse trigonometrical functions

Study Plan

Day 1

36.1 Inverse Trigonometrical functions

36.2 Properties of inverse trigonometrical functions

Day 2

Objective Type Exercise: 1 to 20

Day 3

O.T.E.: 21 to 40

Day 4

O.T.E.: 41 to 60

Day 5

O.T.E.: 61 to 65

Fill in the blanks 1 to 15

Day 6

Fill in the blanks 16 to 25

Practice exercise 1 to 4

Day 7 to 10

Revision

Revision Facilitator

36.1 Inverse Trigonometrical functions

36.2 Properties of inverse trigonometrical functions

Invertible Function - Bijection

Inverse Trigometric Function

Domain and Ranges of Inverse Trigonometric Functions

sin-inv (sin θ) =

Similar relations

sin-inv x = cosec-inv(?)

Similar relations

sin-inv x = cos-inv (?)

Similar relations

sin-inv x + cos-inv x =

Similar relations

sin-inv x + sin-inv y =

Similar relations

sin-inv(-x) =?

Similar relations

2 sin-inv x =?

Similar relations

3 Sin-inv x = ?

Similar relations

Tan-inv x + Tan-inv y + Tan-inv z

Similar relations

36.1 Inverse Trigonometrical functions

36.2 Properties of inverse trigonometrical functions

Study Plan

Day 1

36.1 Inverse Trigonometrical functions

36.2 Properties of inverse trigonometrical functions

Day 2

Objective Type Exercise: 1 to 20

Day 3

O.T.E.: 21 to 40

Day 4

O.T.E.: 41 to 60

Day 5

O.T.E.: 61 to 65

Fill in the blanks 1 to 15

Day 6

Fill in the blanks 16 to 25

Practice exercise 1 to 4

Day 7 to 10

Revision

Revision Facilitator

36.1 Inverse Trigonometrical functions

36.2 Properties of inverse trigonometrical functions

**Recollect the concepts and formulae**Invertible Function - Bijection

Inverse Trigometric Function

Domain and Ranges of Inverse Trigonometric Functions

sin-inv (sin θ) =

Similar relations

sin-inv x = cosec-inv(?)

Similar relations

sin-inv x = cos-inv (?)

Similar relations

sin-inv x + cos-inv x =

Similar relations

sin-inv x + sin-inv y =

Similar relations

sin-inv(-x) =?

Similar relations

2 sin-inv x =?

Similar relations

3 Sin-inv x = ?

Similar relations

Tan-inv x + Tan-inv y + Tan-inv z

Similar relations

### Ch. 37 Solution of Triangles - Revision Facilitator

Sections in the Chapter R D Sharma

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Study Plan

Day 1

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Day 2

Objective Type Exercises 1 to 20

Day 3

Revision

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

a. Right angled triangle - orthocentre

b. Distance of midpoint of the hypotenuse of a right angled triangle from the vertices of the triangle.

c. Relation between mid-point of a right angled triangle and its circumcentre

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Study Plan

Day 1

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

Day 2

Objective Type Exercises 1 to 20

Day 3

Revision

37.1 Solution of Triangles - Concept

37.2 Solution of a right angled triangle

37.3 Solution of a triangle in general

37.4 Some useful results

a. Right angled triangle - orthocentre

b. Distance of midpoint of the hypotenuse of a right angled triangle from the vertices of the triangle.

c. Relation between mid-point of a right angled triangle and its circumcentre

### Ch. 38 Heights and distances - Revision Facilitator

Sections in the chapter R D Sharma

38.1 Angle of elevation and depression of a point

38.2 Some useful results

Study Plan

Day 1

38.1 Angle of elevation and depression of a point

38.2 Some useful results

Day 2

Objective Type Exercises 1 to 20

38.1 Angle of elevation and depression of a point

38.2 Some useful results

Study Plan

Day 1

38.1 Angle of elevation and depression of a point

38.2 Some useful results

Day 2

Objective Type Exercises 1 to 20

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