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Nov 22, 2017

Trigonometrical Ratios of 60° | Trigonometrical Problems | Standard Angles

How to find the Trigonometrical Ratios of 60°? Let a rotating line OX rotates about O in the anti-clockwise sense and starting from its initial position OX traces out ∠XOY = 60° is shown in the

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Nov 22, 2017

Trigonometrical Ratios of 45° | Trigonometrical Problems | Standard Angles

How to find the trigonometrical Ratios of 45°? Suppose a revolving line OX rotates about O in the anti-clockwise sense and starting from the initial position

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Nov 22, 2017

Trigonometrical Ratios of 30° | Trigonometrical Problems | Standard Angles

How to find the trigonometrical Ratios of 30°? Let a rotating line OX rotates about O in the anti-clockwise sense and starting from the initial position OX traces out ∠AOB = 30°.

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Nov 22, 2017

Trigonometrical Ratios of 0° | Trigonometrical Problems | Standard Angles

How to find the Trigonometrical Ratios of 0°? Let a rotating line OX rotates about O in the anti clockwise sense and starting from its initial position OX traces out ∠XOY = θ where θ is very small.

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Nov 21, 2017

Worksheet on Solving a Word Problem by using Linear Equation in One Unknown

Practice the questions given in the worksheet on solving a word problem by using linear equation in one unknown. 1) Sum of two consecutive multiples of five is 85. Find the numbers.

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Nov 20, 2017

Basic Trigonometric Ratios and Their Names |Definitions of Trigonometncal Ratios

To know about the basic trigonometric ratios and their names with respect to a right-angled triangle. Let us consider the right-angled triangle ABO as shown in the adjacent figure.

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Nov 20, 2017

Problems based on S R Theta Formula | s = rθ Formula | S R Theta Formula

Here we will solve two different types of problems based on S R Theta formula. The step-by-step explanation will help us to know how the formula ‘S is Equal to R’ is used to solve these examples.

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Nov 20, 2017

Length of an Arc |S is Equal to R Theta, Diameter of the Circle|Sexagesimal Unit

The examples will help us to understand to how find the length of an arc using the formula of ‘s is equal to r theta’. Worked-out problems on length of an

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Nov 20, 2017

Problems Based on Systems of Measuring Angles | Worked-out Problems

Problems based on systems of measuring angles will help us to learn converting one measuring systems to other measuring systems. We know, the three different systems are Sexagesimal System

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Nov 20, 2017

Convert into Radian | Angle in Circular System | Worked-out Problems

In this topic convert into radian, we will learn how to convert the other units into radian units. The problems are based on changing the different measuring units to radian units.

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Nov 20, 2017

Convert Circular Measure | Circular System to Sexagesimal System

Convert circular measure systems to some other systems. The problems will be converted from circular system to sexagesimal system, circular system to centesimal system and also from circular system

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Nov 20, 2017

Convert the Systems of Measuring Angles |Measuring Angles|Worked-out examples

To convert the systems of measuring angles from one system to the other system. Convert 63°14’51” into circular measure. 63°14'51" = 25299/(400 × 90) Right angle

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Nov 20, 2017

Sexagesimal Centesimal and Circular Systems | Conversion of three Systems

We know, Sexagesimal, Centesimal and Circular Systems are the three different systems of measuring angles. Sexagesimal system is also known as English system and centesimal system is known as French

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Nov 20, 2017

S is Equal to R Theta | Theta Equals S Over R | S R Theta Formula | Radian

Prove that S is equal to r theta, Or,Theta equals s over r. Or, s r theta formula Prove that the radian measure of any angle at the centre of a circle is equal to the ratio of the arc subtending that

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Nov 20, 2017

Important Properties on Circle | A Radian is a Constant Angle|The Greek Letter π

The two important properties on circle are stated below: The ratio of the circumference to the diameter of any circle is constant and the value of this constant is denoted by the Greek letter π.

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Nov 20, 2017

Systems of Measuring Angles | Sexagesimal, Centesimal & Circular System

The following three different systems of units are used in the measurement of trigonometrical angles: Sexagesimal System(or English System), Centesimal System(or French System), Circular System

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Nov 20, 2017

Measure of Angles in Trigonometry | Trigonometrical Angle|Use of Negative Angles

The concept of measure of angles in trigonometry is more general compared to a geometrical angle. More than thousands of years ago, the ancient Babylonians chose 360 as their

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Nov 20, 2017

Trigonometric Angles | Measurement of Triangles | Object of Trigonometry

In mathematics, a very important branch is Trigonometry and in trigonometry one of the important parts is Trigonometric angles. The word ‘Trigonometry’ has been derived from Greek words ‘trigon’

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Nov 20, 2017

Sign of Angles | What is An Angle? | Positive Angle | Negative Angle

Here we will discuss about the sign of angles before that let us recall in brief the definition of an angle. What is an angle? An angle is made up of two rays with a common end point.

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Nov 17, 2017

Problems on Quadratic Equation | Method of Completing the Squares

We will solve different types of problems on quadratic equation using quadratic formula and by method of completing the squares. We know the general form of the quadratic equation

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Nov 17, 2017

Maximum and Minimum Values of the Quadratic Expression | Greatest & Least Values

We will learn how to find the maximum and minimum values of the quadratic Expression ax^2 + bx + c (a ≠ 0). When we find the maximum value and the minimum value of ax^2 + bx + c then let us assume y

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Nov 17, 2017

Sign of the Quadratic Expression | Quadratic Equation | Discriminant

We already acquainted with the general form of quadratic expression ax^2 + bx + c now we will discuss about the sign of the quadratic expression ax^2 + bx + c = 0 (a ≠ 0). When x be real then

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Nov 17, 2017

Theory of Quadratic Equation Formulae | Discriminant of a quadratic equation

The theory of quadratic equation formulae will help us to solve different types of problems on quadratic equation. The general form of a quadratic equation is ax\(^{2}\) + bx + c = 0

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Nov 17, 2017

Condition for Common Root or Roots of Quadratic Equations | One Common Root

We will discuss how to derive the conditions for common root or roots of quadratic equations that can be two or more. Condition for one common root:

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Nov 17, 2017

Symmetric Functions of Roots of a Quadratic Equation | Quadratic Equation

Let α and β be the roots of the quadratic equation ax^2 + bx + c = 0, (a ≠ 0), then the expressions of the form α + β, αβ, α^2 + β^2, α^2 - β^2, 1/α^2 + 1/β^2 etc. are known as functions

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Nov 17, 2017

Irrational Roots of a Quadratic Equation | Surd Roots of a Quadratic Equation

We will discuss about the irrational roots of a quadratic equation. In a quadratic equation with rational coefficients has a irrational or surd root α + √β, where α and β are rational and β is not

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Nov 17, 2017

Complex Roots of a Quadratic Equation | Imaginary Roots of a Quadratic Equation

We will discuss about the complex roots of a quadratic equation. In other words, in a quadratic equation with real coefficients has a complex root α + iβ then it has also the

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Nov 17, 2017

Nature of the Roots of a Quadratic Equation | Discuss the Nature of the Roots

We will discuss here about the different cases of discriminant to understand the nature of the roots of a quadratic equation.

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Nov 16, 2017

Formation of the Quadratic Equation whose Roots are Given | Quadratic Equation

We will learn the formation of the quadratic equation whose roots are given. To form a quadratic equation, let α and β be the two roots. Let us assume that the required equation be ax^2 + bx + c = 0

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Nov 16, 2017

Quadratic Equation cannot have more than Two Roots | Quadratic Equation

We will discuss here that a quadratic equation cannot have more than two roots. Proof: Let us assumed that α, β and γ be three distinct roots of the quadratic equation of the general form

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Nov 16, 2017

Relation between Roots and Coefficients of a Quadratic Equation | Examples

We will learn how to find the relation between roots and coefficients of a quadratic equation. Let us take the quadratic equation of the general form ax^2 + bx + c = 0 where a (≠ 0) is the

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Nov 16, 2017

Quadratic Equation has Only Two Roots | General Form of Quadratic Equation

We will discuss that a quadratic equation has only two roots or in other words we can say that a quadratic equation cannot have more than two roots. We will prove this one-by-one.

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Nov 16, 2017

Introduction of Quadratic Equation | Quadratic Polynomial | General Form

We will discuss about the introduction of quadratic equation. A polynomial of second degree is generally called a quadratic polynomial. If f(x) is a quadratic polynomial, then f(x) = 0 is called

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Nov 16, 2017

Problems on Geometric Progression | Common Ratio of the Geometric Progression

Here we will learn how to solve different types of problems on Geometric Progression. 1. Find the common ratio of the Geometric Progression whose, sum of the third and fifth terms is 90 and its

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Nov 16, 2017

Relation between Arithmetic Means and Geometric Means | Solved Examples

We will discuss here about some of the important relation between Arithmetic Means and Geometric Means. The following properties are: Property I: The Arithmetic Means of two positive numbers

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Nov 16, 2017

Properties of Geometric Progression | Geometric Series | Problems on G. P.

We will discuss about some of the properties of Geometric Progressions and geometric series which we will frequently use in solving different types of problems on Geometric Progressions.

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Nov 16, 2017

Geometric Progression Formulae | General Form of a Geometric Progression

We will discuss about different types of Geometric Progression formulae. 1. The general form of a Geometric Progression is {a, ar, ar^2, ar^3, ar^4, ......}, where ‘a’ and ‘r’ are called the

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Nov 13, 2017

Sum of an infinite Geometric Progression | Geometric Progression | Examples

The sum of an infinite Geometric Progression with first term a and common ratio r (-1 < r < 1 i.e., |r| < 1) is S = a/(1 - r)

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Nov 13, 2017

Selection of Terms in Geometric Progression | Geometric Progression

Sometimes we need to assume certain number of terms in Geometric Progression. The following ways are generally used for the selection of terms in Geometric Progression.

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Nov 13, 2017

Position of a Term in a Geometric Progression | Geometric Sequences

We will learn how to find the position of a term in a Geometric Progression. On finding the position of a given term in a given Geometric Progression We need to use the formula of nth

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Nov 13, 2017

Definition of Geometric Mean | Geometric Progression | Solved Examples

Definition of Geometric Mean: If three quantities are in Geometric Progression then the middle one is called the geometric mean of the other two.

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Nov 13, 2017

Sum of n terms of a Geometric Progression | Find the Sum of the Geometric Series

We will learn how to find the sum of n terms of the Geometric Progression {a, ar, ar^2, ar^3, ar^4, ...........} To prove that the sum of first n terms of the Geometric Progression whose

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Nov 13, 2017

General Form and General Term of a Geometric Progression | nth Term of a P. G.

We will discuss here about the general form and general term of a Geometric Progression. The general form of a Geometric Progression is {a, ar, ar^2, ar^3, .......}, where ‘a’ and ‘r’ are called the

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Nov 13, 2017

Geometric Progression | Geometric Series | Common Ratio | Solved Examples

We will discuss here about the Geometric Progression along with examples. A sequence of numbers is said to be Geometric Progression if the ratio of any term and its preceding term is always a

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Nov 13, 2017

Problems on Sum of 'n' Terms of Arithmetic Progression | Arithmetic Progression

Here we will learn how to solve different types of problems on sum of n terms of Arithmetic Progression. 1. Find the sum of the first 35 terms of an Arithmetic Progression whose third term is 7

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Nov 13, 2017

Problems on Arithmetic Progression | General term of an Arithmetic Progression

Here we will learn how to solve different types of problems on arithmetic progression. 1. Show that the sequence 7, 11, 15, 19, 23, ......... is an Arithmetic Progression. Find its 27th term and the

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Nov 13, 2017

Arithmetic Progression Formulae | General Term of an Arithmetic Progression

We will discuss about different types of Arithmetic Progression formulae. Let ‘a’ be the first term and ‘d’ the common difference of an Arithmetic Progression. Then its General term = a + (n - 1)d

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Nov 12, 2017

Selection of Terms in an Arithmetic Progression | Arithmetic Progression

Sometimes we need to assume certain number of terms in Arithmetic Progression. The following ways are generally used for the selection of terms in an arithmetic progression.

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Nov 12, 2017

Properties of Arithmetic Progression | Problems on Arithmetical Progress

We will discuss about some of the properties of Arithmetic Progression which we will frequently use in solving different types of problems on arithmetical progress. Property I: If a constant

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