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How to find the Trigonometrical Ratios of 60°? Let a rotating line OX rotates about O in the anticlockwise sense and starting from its initial position OX traces out ∠XOY = 60° is shown in the
Continue reading "Trigonometrical Ratios of 60°  Trigonometrical Problems  Standard Angles"
How to find the trigonometrical Ratios of 45°? Suppose a revolving line OX rotates about O in the anticlockwise sense and starting from the initial position
Continue reading "Trigonometrical Ratios of 45°  Trigonometrical Problems  Standard Angles"
How to find the trigonometrical Ratios of 30°? Let a rotating line OX rotates about O in the anticlockwise sense and starting from the initial position OX traces out ∠AOB = 30°.
Continue reading "Trigonometrical Ratios of 30°  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.
Continue reading "Trigonometrical Ratios of 0°  Trigonometrical Problems  Standard Angles"
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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To know about the basic trigonometric ratios and their names with respect to a rightangled triangle. Let us consider the rightangled triangle ABO as shown in the adjacent figure.
Continue reading "Basic Trigonometric Ratios and Their Names Definitions of Trigonometncal Ratios"
Here we will solve two different types of problems based on S R Theta formula. The stepbystep explanation will help us to know how the formula ‘S is Equal to R’ is used to solve these examples.
Continue reading "Problems based on S R Theta Formula  s = rθ Formula  S R Theta Formula"
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’. Workedout problems on length of an
Continue reading "Length of an Arc S is Equal to R Theta, Diameter of the CircleSexagesimal Unit"
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
Continue reading "Problems Based on Systems of Measuring Angles  Workedout 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.
Continue reading "Convert into Radian  Angle in Circular System  Workedout Problems "
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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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
Continue reading "Convert the Systems of Measuring Angles Measuring AnglesWorkedout examples"
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
Continue reading "Sexagesimal Centesimal and Circular Systems  Conversion of three Systems"
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
Continue reading "S is Equal to R Theta  Theta Equals S Over R  S R Theta Formula  Radian"
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.
Continue reading "Important Properties on Circle  A Radian is a Constant AngleThe Greek Letter π"
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
Continue reading "Systems of Measuring Angles  Sexagesimal, Centesimal & Circular System"
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
Continue reading "Measure of Angles in Trigonometry  Trigonometrical AngleUse of Negative Angles"
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’
Continue reading "Trigonometric Angles  Measurement of Triangles  Object of Trigonometry "
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.
Continue reading "Sign of Angles  What is An Angle?  Positive Angle  Negative Angle"
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
Continue reading "Problems on Quadratic Equation  Method of Completing the Squares"
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
Continue reading "Maximum and Minimum Values of the Quadratic Expression  Greatest & Least Values"
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
Continue reading "Sign of the Quadratic Expression  Quadratic Equation  Discriminant"
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
Continue reading "Theory of Quadratic Equation Formulae  Discriminant of a quadratic equation "
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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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
Continue reading "Symmetric Functions of Roots of a Quadratic Equation  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
Continue reading "Irrational Roots of a Quadratic Equation  Surd 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
Continue reading "Complex Roots of a Quadratic Equation  Imaginary Roots of a Quadratic Equation"
We will discuss here about the different cases of discriminant to understand the nature of the roots of a quadratic equation.
Continue reading "Nature of the Roots of a Quadratic Equation  Discuss the Nature of the Roots"
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
Continue reading "Formation of the Quadratic Equation whose Roots are Given  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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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
Continue reading "Relation between Roots and Coefficients of a Quadratic Equation  Examples"
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 onebyone.
Continue reading "Quadratic Equation has Only Two Roots  General Form of Quadratic Equation"
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
Continue reading "Introduction of Quadratic Equation  Quadratic Polynomial  General Form"
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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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
Continue reading "Relation between Arithmetic Means and Geometric Means  Solved Examples"
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.
Continue reading "Properties of Geometric Progression  Geometric Series  Problems on G. P."
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
Continue reading "Geometric Progression Formulae  General Form of a Geometric Progression "
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)
Continue reading "Sum of an infinite Geometric Progression  Geometric Progression  Examples"
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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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
Continue reading "Position of a Term in a Geometric Progression  Geometric Sequences"
Definition of Geometric Mean: If three quantities are in Geometric Progression then the middle one is called the geometric mean of the other two.
Continue reading "Definition of Geometric Mean  Geometric Progression  Solved Examples"
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
Continue reading "Sum of n terms of a Geometric Progression  Find the Sum of the Geometric Series"
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
Continue reading "General Form and General Term of a Geometric Progression  nth Term of a P. G."
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
Continue reading "Geometric Progression  Geometric Series  Common Ratio  Solved Examples"
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
Continue reading "Problems on Sum of 'n' Terms of Arithmetic Progression  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
Continue reading "Problems on Arithmetic Progression  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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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.
Continue reading "Selection of Terms in an Arithmetic Progression  Arithmetic Progression"
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
Continue reading "Properties of Arithmetic Progression  Problems on Arithmetical Progress"
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