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





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

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



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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

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

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

Ch. 1. Sets - Concept Review


Mathematicians encountered server difficulties in defining set. They realized that there is a need for some undefined (primitive) terms. Thus set and elements are undefined terms in mathematics.

Set is synonymous with the words, ‘collection’, aggregate’, ‘class’, and is comprised of elements.

The words ‘element’, ‘object’, and ‘member’ are synonymous.

Sets designated by specific letters.

N: natural numbers
Z : integers
Z+: positive integers
Q: rational numbers
Q+: positive rational numbers
R: real numbers
R+: positive real numbers
C: complex numbers


Description of a set

Sets can be described by roster method or set-builder method.


Types of sets

Empty set
Singleton set
Finite set
Infinite set
Equivalent set
Equal set
Subset
Universal set
Power set

Theorems on subsets

1. Every set is a subset of itself.
2. The empty set is a subset of every set.
3. The total number of subsets of a finite set containing n elements is 2ⁿ

1.7 Venn Diagrams

In Venn diagrams the universal set U is represented by points within a rectangle and its subsets are represented by points in closed curves (usually circles) within the the rectangle. If two sets A and B have some common elements, they will be shown two intersecting circles. If the two sets are disjointed sets, then they are represented by two non-intersecting circles. If set B is a subset of A,  then B is shown as a circle inside the circle representing set A.


1.8 Operations on Sets

Union of Sets

Intersection of Sets

Difference of Sets

Symmetric Difference of Two Sets

Disjoint Sets

Complement of a Set

1.9 Laws of algebra of sets


1. Idempotent laws

(i) A U A = A
(ii) A ∩ A = A

2. Identity laws

(i) A U ф = A
(ii) A ∩ U = A

3. commutative law
(i) A U B = B U A
(ii) A ∩ B = B ∩ A

4. Associative laws

(i) (A U B) U C = A U (B U C)
(ii) (A ∩ B) ∩ C = A ∩ (B ∩ C)

5. Distributive laws

(i) A U (B ∩ C) = (A U B) ∩ (A U C)
(ii) A ∩ (B U C) = (A ∩ B) U (A ∩ C)

6. De-morgan’s laws

(i) (A U B)’ = A’ ∩ B’
(ii) (A ∩ B)’ = A’ U B’

1.10 Some more theorems

If A and B are two sets

(i) A – B = A ∩ B’
(ii) B – A = B ∩ A’
(iii) A – B = A  A ∩ B = ф
(iv) (A – B) U B = A U B
(v) (A-B) ∩ B = ф
(vi) A is a sub set of B  B’ is a subset of A’
(vii) (A-B) U (B-A) = (A U B) – (A ∩ B)

If A, B and C are three sets, then

(i) A – (B ∩ C) = (A-B) U (A-C)
(ii) A – (B U C) = (A-B) ∩ (A-C)
(iii) A ∩ (B-C) = (A ∩ B) - (A ∩ C)
(iv) A ∩ (B Δ C) = (A∩B) Δ (A∩C)