# Math Blog

### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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

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

### 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

### 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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### 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

### 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

### 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

### 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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### 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

### 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

### 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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### 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.

###### Nov 16, 2017

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

### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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