Math Blog
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Newly added pages can be seen from this page. Keep visiting to this page so that you will remain updated.en-usMathWed, 25 Apr 2018 18:57:15 -0400Wed, 25 Apr 2018 18:57:15 -0400math-only-math.comApr 25, Square Matrix | Definition of Square Matrix |Diagonal of Square Matrix
http://www.math-only-math.com/square-matrix.html6c779670e44a64a7c93fd0e876917e2aIf square matrixes have n rows or columns then the matrix is called the square matrix of order n or an n-square matrix. Definition of Square Matrix: An n × n matrix is said to be a square matrix of order n. In other words when the number of rows and the number of columns inWed, 25 Apr 2018 18:57:13 -0400Apr 25, Matrix | Definition of a Matrix | Examples of a Matrix | Elements
http://www.math-only-math.com/matrix.html569e4435a035f033b770a662ac5b360bA rectangular array of mn elements aij into m rows and n columns, where the elements aij belongs to field F, is said to be a matrix of order m × n (or an m × n matrix) over the field F. Definition of a Matrix: A matrix is a rectangular arrangement or array of numbersWed, 25 Apr 2018 17:53:52 -0400Mar 30, Joint Variation | Solving Joint Variation Problems and Application
http://www.math-only-math.com/joint-variation.html35e8acacf3082a6e9c71339de78b93dcOne variable quantity is said to vary jointly as a number of other variable quantities, when it varies directly as their product. If the variable A varies directly as the product of the variables B, C and D, i.e., if.A ∝ BCD or A = kBCD (k = constant ), then A varies jointlyFri, 30 Mar 2018 19:32:26 -0400Mar 30, Indirect Variation | Inverse Variation | Inverse or Indirect Variation
http://www.math-only-math.com/indirect-variation.html382930d172f9752abd7fd42df938aedfWhen two variables change in inverse proportion it is called as indirect variation. In indirect variation one variable is constant times inverse of other. If one variable increases other will decrease, if one decrease other will also increase. This means that the variablesFri, 30 Mar 2018 17:27:33 -0400Mar 26, Direct Variation | Solving Direct Variation Word Problem
http://www.math-only-math.com/direct-variation-problems.html1d1bafed1c06a2a324c0493720c252c1When two variables change in proportion it is called as direct variation. In direct variation one variable is constant times of other. If one variable increases other will increase, if one decrease other will also decease. This means that the variables change in a same ratioMon, 26 Mar 2018 17:29:51 -0400Mar 25, Methods of Solving Simultaneous Linear Equations | Solved Examples
http://www.math-only-math.com/methods-of-solving-simultaneous-linear-equations.html50f4dfd99dcec2a59675a1b915a5a7ddThere are different methods for solving simultaneous linear Equations: 1. Elimination of a variable 2. Substitution 3. Cross-multiplication 4. Evaluation of proportional value of variables This topic is purely based upon numerical examples. So, let us solve some examplesSun, 25 Mar 2018 17:36:18 -0400Mar 24, Method of Cross Multiplication|Solve by Method of Cross Multiplication
http://www.math-only-math.com/method-of-cross-multiplication.html5994a32337b7f63c167a58954dd8af3cThe next method of solving linear equations in two variables that we are going to learn about is method of cross multiplication. Let us see the steps followed while soling the linear equation by method of cross multiplication: Assume two linear equation be A1 x + B1y + C1= Sat, 24 Mar 2018 16:12:15 -0400Mar 6, Properties of Angles of a Triangle |Sum of Three Angles of a Triangle
http://www.math-only-math.com/properties-of-angles-of-a-triangle.html20dfdeb18fea0ae94526972015760114We will discuss about some of the properties of angles of a triangle. 1. The three angles of a triangle are together equal to two right angles. ABC is a triangle. Then ∠ZXY + ∠XYZ + ∠YZX = 180° Using this property, let us solve some of the examples. Solved examplesTue, 6 Mar 2018 15:21:47 -0500Mar 2, Geometrical Property of Altitudes|Altitudes of Triangle are Concurrent
http://www.math-only-math.com/geometrical-property-of-altitudes.html8110a1f91f66645ddb11079884e4f154The three altitudes of triangle are concurrent. The point at which they intersect is known as the orthocentre of the triangle. In the adjoining figure, the three altitudes XP, YQ and ZR intersect at the orthocentre O.Fri, 2 Mar 2018 17:39:10 -0500Mar 1, Medians and Altitudes of a Triangle |Three Altitudes and Three Medians
http://www.math-only-math.com/medians-and-altitudes-of-a-triangle.html5a2be812dd56b9df57d1d060d1a24930Here we will discuss about Medians and Altitudes of a Triangle. Median: The straight line joining a vertex of a triangle to the midpoint of the opposite side is called a median. A triangle has three medians. Here XL, YM and ZN are medians. A geometrical property of mediansThu, 1 Mar 2018 18:02:44 -0500Feb 28, Classification of Triangles on the Basis of Their Sides and Angles
http://www.math-only-math.com/classification-of-triangles.html94d39302c9c2dabed9e2425d51433d38Here we will discuss about classification of triangles on the basis of their sides and angles Equilateral triangle: An equilateral triangle is a triangle whose all three sides are equal. Here, XYZ is an equilateral triangle as XY = YZ = ZX. Isosceles triangle: An isoscelesWed, 28 Feb 2018 17:28:16 -0500Feb 22, Triangle | Exterior Opposite Angles|Interior Opposite Angles|Perimeter
http://www.math-only-math.com/triangle.html91198bc0b76bf73be2a273a9bbe517c2A triangle is a plane figure bounded by three straight lines. A triangle has three sides and three angles, and each one of them is called an element of the triangle. Here, PQR is a triangle, its three sides are line segments PQ, QR and RP; ; ∠PQR, ∠QRP and ∠RPQ are itsThu, 22 Feb 2018 13:41:09 -0500Feb 14, Problem on Change the Subject of a Formula | Changing the Subject
http://www.math-only-math.com/problem-on-change-the-subject-of-a-formula.html5e3b3f9e47dfe26ec9ce3978aba5ee89We will solve different types of problems on change the subject of a formula. The subject of a formula is a variable whose relation with other variables of the context is sought and the formula is written in such a way that subject is expressed in terms of the otherWed, 14 Feb 2018 16:29:23 -0500Feb 13, Worksheet on Change of Subject | Change the Subject as Indicated
http://www.math-only-math.com/worksheet-on-change-of-subject.html6a1042736b7ef0ff95515b68dd740df1Practice the questions given in the worksheet on change of subject When a formula involving certain variables is known, we can change the subject of the formula. What is the subject in each of the following questions? Change the subject as indicated.Tue, 13 Feb 2018 15:31:53 -0500Feb 2, Worksheet on Framing a Formula | Framing Formulas | Frame an Equation
http://www.math-only-math.com/worksheet-on-framing-a-formula.html5d5d6e1bfe006fe5203f8ed80ce4530fPractice the questions given in the worksheet on framing a formula. I. Frame a formula for each of the following statements: 1. The side ‛s’ of a square is equal to the square root of its area A.Fri, 2 Feb 2018 15:55:02 -0500Jan 31, Establishing an Equation | Framing a Formula | Framing Linear Equation
http://www.math-only-math.com/establishing-an-equation.html4d96b4d3b2fc29a8185ea309d10d1ef1We will discuss here about establishing an equation. In a given context, the relation between variables expressed by equality (or inequality) is called a formula. When a formula is expressed by an equality, the algebraic expression is called an equation.Wed, 31 Jan 2018 16:22:25 -0500Jan 22, Rectangular Cartesian Co-ordinates | Abscissa | Ordinate | Oblique Co-ordinate
http://www.math-only-math.com/rectangular-cartesian-co-ordinates.html66a38fb1df289d3545c4e6fd7d1103c4What is Rectangular Cartesian Co-ordinates? Let O be a fixed point on the plane of this page; draw mutually perpendicular straight line XOX’ and YOY’ through O. Clearly, these lines divide the planeMon, 22 Jan 2018 17:10:33 -0500Jan 21, What is Co-ordinate Geometry? | Analytical Geometry| Cartesian Co-ordinate
http://www.math-only-math.com/co-ordinate-geometry.htmld6e038081e2b274e11be160eb87c186dWhat is co-ordinate geometry? The subject <b>co-ordinate geometry</b> is that particular branch of mathematics in which geometry is studied with the help of algebra. This branch of mathematics was firSun, 21 Jan 2018 14:44:35 -0500Jan 20, Table of Tangents and Cotangents | Natural Tangents and Natural Cotangents
http://www.math-only-math.com/table-of-tangents-and-cotangents.htmlbd841d8ee58243fe18d7ce0e3730d645We will discuss here the method of using the table of tangents and cotangents. This table shown below is also known as the table of natural tangents and natural cotangents. Using the table we canSat, 20 Jan 2018 15:15:23 -0500Jan 20, Table of Sines and Cosines |Trigonometric Table|Table of Natural sines & cosines
http://www.math-only-math.com/table-of-sines-and-cosines.html14095676c9fb3de1593a6c43981482e2We will discuss here the method of using the table of sines and cosines: The above table is also known as the table of natural sines and natural cosines. Using the table we can find the valuesSat, 20 Jan 2018 15:11:27 -0500Jan 20, Problems on Properties of Triangle | Angle Properties of Triangles
http://www.math-only-math.com/problems-on-properties-of-triangle.htmld77c67e96b0bb48c29b54a6e93395be8We will solve different types of problems on properties of triangle. 1. If in any triangle the angles be to one another as 1 : 2 : 3, prove that the corresponding sides are 1 : √3 : 2.Sat, 20 Jan 2018 15:05:28 -0500Jan 20, Properties of Triangle Formulae | Triangle Formulae | Properties of Triangle
http://www.math-only-math.com/properties-of-triangle-formulae.html44cf1383fe030763b6c5f9d587ef5c1cWe will discuss the list of properties of triangle formulae which will help us to solve different types of problems on triangle.Sat, 20 Jan 2018 15:01:42 -0500Jan 20, Law of Tangents |The Tangent Rule|Proof of the Law of Tangents|Alternative Proof
http://www.math-only-math.com/law-of-tangents.htmlad24e745054693365f751d1af7f1a4e5We will discuss here about the law of tangents or the tangent rule which is required for solving the problems on triangle. In any triangle ABC,Sat, 20 Jan 2018 14:55:51 -0500Jan 20, Area of a Triangle | ∆ = ½ bc sin A | ∆ = ½ ca sin B | ∆ = ½ ab sin C
http://www.math-only-math.com/area-of-a-triangle.html9c917d30b4018b6a01541fbe3b1710eeIf ∆ be the area of a triangle ABC, Proved that, ∆ = ½ bc sin A = ½ ca sin B = ½ ab sin C That is, (i) ∆ = ½ bc sin A (ii) ∆ = ½ ca sin B (iii) ∆ = ½ ab sin CSat, 20 Jan 2018 14:49:20 -0500Jan 20, The Law of Cosines | The Cosine Rule | Cosine Rule Formula | Cosine Law Proof
http://www.math-only-math.com/law-of-cosines.html30620ccc8d897874ebff2733a5f4eb3bWe will discuss here about the law of cosines or the cosine rule which is required for solving the problems on triangle. In any triangle ABC, Prove that, (i) b\(^{2}\)Sat, 20 Jan 2018 14:42:53 -0500Jan 20, Proof of Projection Formulae | Projection Formulae | Geometrical Interpretation
http://www.math-only-math.com/proof-of-projection-formulae.htmlf89ffaae0e4d78aaaf164cecbcfa1f4aThe geometrical interpretation of the proof of projection formulae is the length of any side of a triangle is equal to the algebraic sum of the projections of other sides upon it. In Any TriangleSat, 20 Jan 2018 14:33:02 -0500Jan 20, Projection Formulae | a = b cos C + c cos B | b = c cos A + a cos C
http://www.math-only-math.com/projection-formulae.html2b9965e0df16d9b1e94f330411659063Projection formulae is the length of any side of a triangle is equal to the sum of the projections of other two sides on it. In Any Triangle ABC, (i) a = b cos C + c cos BSat, 20 Jan 2018 14:25:09 -0500Jan 20, Theorem on Properties of Triangle | p/sin P = q/sin Q = r/sin R = 2K
http://www.math-only-math.com/theorem-on-properties-of-triangle.htmlc92b0f84d7f166b49627bf57c0f7769dProof the theorem on properties of triangle p/sin P = q/sin Q = r/sin R = 2K. Proof: Let O be the circum-centre and R the circum-radius of any triangle PQR. Let O be the circum-centre and R Sat, 20 Jan 2018 13:52:40 -0500Jan 20, The Law of Sines | The Sine Rule | The Sine Rule Formula | Law of sines Proof
http://www.math-only-math.com/law-of-sines.html7676bd9b86dc0c01d5bcfff846f95c70We will discuss here about the law of sines or the sine rule which is required for solving the problems on triangle. In any triangle the sides of a triangle are proportional to the sinesSat, 20 Jan 2018 13:38:42 -0500Jan 20, Properties of Triangles | Semi-perimeter| Circum-circle|Circum-radius|In-radius
http://www.math-only-math.com/properties-of-triangles.html01e1050e7f432d9ba5ea61f96cdb88c9In trigonometry we will discuss about the different properties of triangles. We know any triangle has six parts, the three sides and the three angles are generally called the elements of the triangle.Sat, 20 Jan 2018 13:25:25 -0500Jan 19, Problems on Inverse Trigonometric Function | Inverse Circular Function Problems
http://www.math-only-math.com/problems-on-inverse-trigonometric-function.html61fe0c6c1534cea1b1697920cf5102b6We will solve different types of problems on inverse trigonometric function. 1. Find the values of sin (cos\(^{-1}\) 3/5) Fri, 19 Jan 2018 17:12:23 -0500Jan 19, Principal Values of Inverse Trigonometric Functions |Different types of Problems
http://www.math-only-math.com/principal-values-of-inverse-trigonometric-functions.html54d94705acb3936989eccd390a99413bWe will learn how to find the principal values of inverse trigonometric functions in different types of problems. The principal value of sin\(^{-1}\) x for x > 0, is the length of the arc of a unitFri, 19 Jan 2018 16:54:48 -0500Jan 19, Inverse Trigonometric Function Formula | Inverse Circular Function Formula
http://www.math-only-math.com/inverse-trigonometric-function-formula.html0a9495fe73652f0016c9f4e133526051We will discuss the list of inverse trigonometric function formula which will help us to solve different types of inverse circular or inverse trigonometric function.Fri, 19 Jan 2018 16:49:10 -0500Jan 19, 3 arctan(x) | 3 tan\(^{-1}\) x |3 tan inverse x | Inverse Trigonometric Function
http://www.math-only-math.com/3-arctan-x.html775447817fa1f004afd315daaccab6a3We will learn how to prove the property of the inverse trigonometric function 3 arctan(x) = arctan(\(\frac{3x - x^{3}}{1 - 3 x^{2}}\)) or, 3 tan\(^{-1}\) x = tan\(^{-1}\)Fri, 19 Jan 2018 16:41:31 -0500Jan 19, 3 arccos(x) | 3 cos\(^{-1}\) x |3 cos inverse x | Inverse Trigonometric Function
http://www.math-only-math.com/3-arccos-x.html6e86c99db5c8d3d2db0105a639800fcbWe will learn how to prove the property of the inverse trigonometric function 3 arccos(x) = arccos(4x\(^{3}\) - 3x) or, 3 cos\(^{-1}\) x = cos\(^{-1}\) (4x\(^{3}\) - 3x)Fri, 19 Jan 2018 16:38:57 -0500Jan 19, 3 arcsin(x) | 3 sin\(^{-1}\) x |3 sin inverse x | Inverse Trigonometric Function
http://www.math-only-math.com/3-arcsin-x.html82deaf78ef4faf3232b95a5a0bcc5f7aWe will learn how to prove the property of the inverse trigonometric function 3 arcsin(x) = arcsin(3x - 4x\(^{3}\)) or, 3 sin\(^{-1}\) x = sin\(^{-1}\) (3x - 4x\(^{3}\))Fri, 19 Jan 2018 16:32:30 -0500Jan 19, 2 arctan(x) | 2 tan\(^{-1}\) x | 2 tan inverse x |Inverse Trigonometric Function
http://www.math-only-math.com/2-arctan-x.htmlc1aadf0ecca7e624cebbee68d21f8fb8We will learn how to prove the property of the inverse trigonometric function, 2 arctan(x) = arctan(\(\frac{2x}{1 - x^{2}}\)) = arcsin(\(\frac{2x}{1 + x^{2}}\))Fri, 19 Jan 2018 16:20:02 -0500Jan 19, 2 arccos(x) | 2 cos\(^{-1}\) x | 2 cos inverse x |Inverse Trigonometric Function
http://www.math-only-math.com/2-arccos-x.htmld596b9d8f70ef341163cd0fb7adc553eWe will learn how to prove the property of the inverse trigonometric function 2 cos\(^{-1}\) x = cos\(^{-1}\) (2x\(^{2}\) - 1) or, 2 arccos(x) = arccos(2x\(^{2}\) - 1).Fri, 19 Jan 2018 15:56:56 -0500Jan 19, 2 arcsin(x) | 2 sin\(^{-1}\) x | 2 sin inverse x |Inverse Trigonometric Function
http://www.math-only-math.com/2-arcsin-x.html3aebe8a2b34cb5358a06cb95d5da8bb7We will learn how to prove the property of the inverse trigonometric function 2 arcsin(x) = arcsin(2x\(\sqrt{1 - x^{2}}\)) or, 2 sin\(^{-1}\) x = sin\(^{-1}\) (2x\(\sqrt{1 - x^{2}}\))Fri, 19 Jan 2018 15:54:21 -0500Jan 19, arccos(x) - arccos(y) | cos^-1 x - cos^-1 y | Inverse Trigonometric Function
http://www.math-only-math.com/arccos-x-minus-arccos-y.html2afb12f0cdd60265008533931466f607We will learn how to prove the property of the inverse trigonometric function arccos(x) - arccos(y) = arccos(xy + \(\sqrt{1 - x^{2}}\)\(\sqrt{1 - y^{2}}\))Fri, 19 Jan 2018 15:46:30 -0500Jan 19, arccos(x) + arccos(y) | cos^-1 x + cos^-1 y | Inverse Trigonometric Function
http://www.math-only-math.com/arccos-x-plus-arccos-y.html1283d4eab074f9d88d7a952012824386We will learn how to prove the property of the inverse trigonometric function arccos (x) + arccos(y) = arccos(xy - \(\sqrt{1 - x^{2}}\)\(\sqrt{1 - y^{2}}\))Fri, 19 Jan 2018 15:41:50 -0500Jan 19, arcsin x - arcsin y |sin\(^{-1}\) x - sin\(^{-1}\) y|sin inverse x-sin inverse y
http://www.math-only-math.com/arcsin-x-minus-arcsin-y.html7d1b1a8032e803ad1068e3dac61a8958We will learn how to prove the property of the inverse trigonometric function arcsin (x) - arcsin(y) = arcsin (x \(\sqrt{1 - y^{2}}\) - y\(\sqrt{1 - x^{2}}\))Fri, 19 Jan 2018 15:33:33 -0500Jan 18, arcsin(x) + arcsin(y) |sin\(^{-1}\) x+sin\(^{-1}\) y|sin inverse x+sin inverse y
http://www.math-only-math.com/arcsin-x-plus-arcsin-y.html6ec83f7a688330dccc1195aff5cabdcfWe will learn how to prove the property of the inverse trigonometric function arcsin (x) + arcsin(y) = arcsin (x \(\sqrt{1 - y^{2}}\) + y\(\sqrt{1 - x^{2}}\))Thu, 18 Jan 2018 15:34:45 -0500Jan 18, arccot(x) - arccot(y) | cot^-1 x - cot^-1 y | Inverse Trigonometric Function
http://www.math-only-math.com/arccot-x-minus-arccot-y.html9d480fde74e4aaefb4b5b8a715b65aafWe will learn how to prove the property of the inverse trigonometric function arccot(x) - arccot(y) = arccot(\(\frac{xy + 1}{y - x}\)) (i.e., cot\(^{-1}\) x + cot\(^{-1}\) y = cot\(^{-1}\)Thu, 18 Jan 2018 15:29:21 -0500Jan 18, arccot(x) + arccot(y) | cot^-1 x + cot^-1 y | Inverse Trigonometric Function
http://www.math-only-math.com/arccot-x-plus-arccot-y.htmlcaf16ebb024180bec1360a30d4149cfeWe will learn how to prove the property of the inverse trigonometric function arccot(x) + arccot(y) = arccot(\(\frac{xy - 1}{y + x}\)) (i.e., cot\(^{-1}\) x - cot\(^{-1}\) y = cot\(^{-1}\)Thu, 18 Jan 2018 14:00:20 -0500Jan 16, arctan(x) + arctan(y) + arctan(z) | tan^-1 x + tan^-1 y + tan^-1 z |Inverse Trig
http://www.math-only-math.com/arctan-x-plus-arctan-y-plus-arctan-z.htmla6e41690b2d9958a9b90fd0c7d392292We will learn how to prove the property of the inverse trigonometric function arctan(x) + arctan(y) + arctan(z) = arctan\(\frac{x + y + z – xyz}{1 – xy – yz – zx}\) (i.e., tan\(^{-1}\) xTue, 16 Jan 2018 17:09:16 -0500Jan 16, arctan x + arccot x = π/2 | arctan(x) + arccot(x) = \(\frac{π}{2}\) | Examples
http://www.math-only-math.com/arctan-x-plus-arccot-x-equals-pi-by-2.html4fd890a8fe962e19f6a24ad0aab7f286We will learn how to prove the property of the inverse trigonometric function arctan(x) + arccot(x) = \(\frac{π}{2}\) (i.e., tan\(^{-1}\) x + cot\(^{-1}\) x = \(\frac{π}{2}\)).Tue, 16 Jan 2018 17:06:45 -0500Jan 16, arctan x - arctan y | tan^-1 x - tan^-1 y | Inverse Trigonometric Function
http://www.math-only-math.com/arctan-x-minus-arctan-y.htmlb8d08fdb3acddba56050ffe4f02f00eeWe will learn how to prove the property of the inverse trigonometric function arctan(x) - arctan(y) = arctan(\(\frac{x - y}{1 + xy}\)) (i.e., tan\(^{-1}\) x - tan\(^{-1}\) yTue, 16 Jan 2018 17:04:04 -0500Jan 16, arctan(x) + arctan(y) = arctan(\(\frac{x + y}{1 - xy}\)) | tan^-1 x + tan^-1 y
http://www.math-only-math.com/arctan-x-plus-arctan-y.html19d876755a11cc269f2f028e14847b10We will learn how to prove the property of the inverse trigonometric function arctan(x) + arctan(y) = arctan(\(\frac{x + y}{1 - xy}\)), (i.e., tan\(^{-1}\) x + tan\(^{-1}\) y = tan\(^{-1}\)Tue, 16 Jan 2018 16:15:20 -0500Jan 15, Method of Substitution | The Substitution Method Examples
http://www.math-only-math.com/method-of-substitution.html45bac4490d40b59e173191a2c85fc9eeSteps involved in solving linear equations in two variables by method of substitution: Examine the question carefully and make sure that two different lineMon, 15 Jan 2018 15:44:51 -0500Jan 14, arcsin x + arccos x = π/2 | arcsin(x) + arccos(x) = \(\frac{π}{2}\) | Examples
http://www.math-only-math.com/arcsin-x-plus-arccos-x-equals-pi-by-2.html7ebd3451c09cfcf180c6982df29802e7We will learn how to prove the property of the inverse trigonometric function arcsin(x) + arccos(x) = \(\frac{π}{2}\). Proof: Let, sin\(^{-1}\) x = θ Therefore, x = sin θ Sun, 14 Jan 2018 16:28:13 -0500Jan 14, General Values of Inverse Trigonometric Functions | Inverse Circular Functions
http://www.math-only-math.com/general-values-of-inverse-trigonometric-functions.html07ab7863d8d89e5091befc2d8beb8fdbWe will learn how to find the general values of inverse trigonometric functions in different types of problems. 1. Find the general values of sin\(^{-1}\) (- √3/2)Sun, 14 Jan 2018 16:20:59 -0500