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We 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 other
Continue reading "Problem on Change the Subject of a Formula  Changing the Subject"
Practice 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.
Continue reading "Worksheet on Change of Subject  Change the Subject as Indicated"
Practice 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.
Continue reading "Worksheet on Framing a Formula  Framing Formulas  Frame an Equation"
We 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.
Continue reading "Establishing an Equation  Framing a Formula  Framing Linear Equation"
What is Rectangular Cartesian Coordinates? 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 plane
Continue reading "Rectangular Cartesian Coordinates  Abscissa  Ordinate  Oblique Coordinate "
What is coordinate geometry? The subject coordinate geometry is that particular branch of mathematics in which geometry is studied with the help of algebra. This branch of mathematics was fir
Continue reading "What is Coordinate Geometry?  Analytical Geometry Cartesian Coordinate"
We 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 can
Continue reading "Table of Tangents and Cotangents  Natural Tangents and Natural Cotangents "
We 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 values
Continue reading "Table of Sines and Cosines Trigonometric TableTable of Natural sines & cosines"
We 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.
Continue reading "Problems on Properties of Triangle  Angle Properties of Triangles"
We will discuss the list of properties of triangle formulae which will help us to solve different types of problems on triangle.
Continue reading "Properties of Triangle Formulae  Triangle Formulae  Properties of Triangle"
We 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,
Continue reading "Law of Tangents The Tangent RuleProof of the Law of TangentsAlternative Proof"
If ∆ 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 C
Continue reading "Area of a Triangle  ∆ = ½ bc sin A  ∆ = ½ ca sin B  ∆ = ½ ab sin C"
We 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\(^{2}\)
Continue reading "The Law of Cosines  The Cosine Rule  Cosine Rule Formula  Cosine Law Proof"
The 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 Triangle
Continue reading "Proof of Projection Formulae  Projection Formulae  Geometrical Interpretation "
Projection 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 B
Continue reading "Projection Formulae  a = b cos C + c cos B  b = c cos A + a cos C"
Proof the theorem on properties of triangle p/sin P = q/sin Q = r/sin R = 2K. Proof: Let O be the circumcentre and R the circumradius of any triangle PQR. Let O be the circumcentre and R
Continue reading "Theorem on Properties of Triangle  p/sin P = q/sin Q = r/sin R = 2K"
We 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 sines
Continue reading "The Law of Sines  The Sine Rule  The Sine Rule Formula  Law of sines Proof"
In 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.
Continue reading "Properties of Triangles  Semiperimeter CircumcircleCircumradiusInradius "
We will solve different types of problems on inverse trigonometric function. 1. Find the values of sin (cos\(^{1}\) 3/5)
Continue reading "Problems on Inverse Trigonometric Function  Inverse Circular Function Problems"
We 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 unit
Continue reading "Principal Values of Inverse Trigonometric Functions Different types of Problems"
We will discuss the list of inverse trigonometric function formula which will help us to solve different types of inverse circular or inverse trigonometric function.
Continue reading "Inverse Trigonometric Function Formula  Inverse Circular Function Formula"
We 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\(^{1}\)
Continue reading "3 arctan(x)  3 tan\(^{1}\) x 3 tan inverse x  Inverse Trigonometric Function"
We 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)
Continue reading "3 arccos(x)  3 cos\(^{1}\) x 3 cos inverse x  Inverse Trigonometric Function"
We 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\(^{3}\))
Continue reading "3 arcsin(x)  3 sin\(^{1}\) x 3 sin inverse x  Inverse Trigonometric Function"
We will learn how to prove the property of the inverse trigonometric function, 2 arctan(x) = arctan(\(\frac{2x}{1  x^{2}}\)) = arcsin(\(\frac{2x}{1 + x^{2}}\))
Continue reading "2 arctan(x)  2 tan\(^{1}\) x  2 tan inverse x Inverse Trigonometric Function"
We 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).
Continue reading "2 arccos(x)  2 cos\(^{1}\) x  2 cos inverse x Inverse Trigonometric Function"
We 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\(\sqrt{1  x^{2}}\))
Continue reading "2 arcsin(x)  2 sin\(^{1}\) x  2 sin inverse x Inverse Trigonometric Function"
We will learn how to prove the property of the inverse trigonometric function arccos(x)  arccos(y) = arccos(xy + \(\sqrt{1  x^{2}}\)\(\sqrt{1  y^{2}}\))
Continue reading "arccos(x)  arccos(y)  cos^1 x  cos^1 y  Inverse Trigonometric Function"
We will learn how to prove the property of the inverse trigonometric function arccos (x) + arccos(y) = arccos(xy  \(\sqrt{1  x^{2}}\)\(\sqrt{1  y^{2}}\))
Continue reading "arccos(x) + arccos(y)  cos^1 x + cos^1 y  Inverse Trigonometric Function"
We will learn how to prove the property of the inverse trigonometric function arcsin (x)  arcsin(y) = arcsin (x \(\sqrt{1  y^{2}}\)  y\(\sqrt{1  x^{2}}\))
Continue reading "arcsin x  arcsin y sin\(^{1}\) x  sin\(^{1}\) ysin inverse xsin inverse y"
We will learn how to prove the property of the inverse trigonometric function arcsin (x) + arcsin(y) = arcsin (x \(\sqrt{1  y^{2}}\) + y\(\sqrt{1  x^{2}}\))
Continue reading "arcsin(x) + arcsin(y) sin\(^{1}\) x+sin\(^{1}\) ysin inverse x+sin inverse y"
We 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\(^{1}\)
Continue reading "arccot(x)  arccot(y)  cot^1 x  cot^1 y  Inverse Trigonometric Function"
We 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\(^{1}\)
Continue reading "arccot(x) + arccot(y)  cot^1 x + cot^1 y  Inverse Trigonometric Function "
We 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\(^{1}\) x
Continue reading "arctan(x) + arctan(y) + arctan(z)  tan^1 x + tan^1 y + tan^1 z Inverse Trig"
We 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 = \(\frac{π}{2}\)).
Continue reading "arctan x + arccot x = π/2  arctan(x) + arccot(x) = \(\frac{π}{2}\)  Examples"
We 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
Continue reading "arctan x  arctan y  tan^1 x  tan^1 y  Inverse Trigonometric Function"
We 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\(^{1}\)
Continue reading "arctan(x) + arctan(y) = arctan(\(\frac{x + y}{1  xy}\))  tan^1 x + tan^1 y"
Steps involved in solving linear equations in two variables by method of substitution: Examine the question carefully and make sure that two different line
Continue reading "Method of Substitution  The Substitution Method Examples"
We 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
Continue reading "arcsin x + arccos x = π/2  arcsin(x) + arccos(x) = \(\frac{π}{2}\)  Examples"
We 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)
Continue reading "General Values of Inverse Trigonometric Functions  Inverse Circular Functions "
How to find the general and principal values of cot\(^{1}\) x? Let cot θ = x ( ∞ < x < ∞) then θ = cot\(^{1}\) x. Here θ has infinitely many values.
Continue reading "General and Principal Values of cot\(^{1}\) x  Inverse Circular Functions"
How to find the general and principal values of sec\(^{1}\) x? Let sec θ = x ( I x I ≥ 1 i.e., x ≥ 1 or, x ≤  1 ) then θ = sec  1x . Here θ has infinitely many values.
Continue reading "General and Principal Values of sec\(^{1}\) x  General values of arc sec x"
How to find the general and principal values of ccs\(^{1}\) x? Let csc θ = x ( I x I ≥ 1 i.e., x ≥ 1 or, x ≤  1 ) then θ = csc  1x . Here θ has infinitely many values.
Continue reading "General and Principal Values of csc\(^{1}\) x  Inverse Circular Functions"
How to find the general and principal values of tan\(^{1}\) x? Let tan θ = x ( ∞ < x < ∞) then θ = tan\(^{1}\) x. Here θ has infinitely many values.
Continue reading "General and Principal Values of tan\(^{1}\) x  Inverse Circular Functions"
How to find the general and principal values of cos\(^{1}\) x? Let cos θ = x where, ( 1 ≤ x ≤ 1) then θ = cos\(^{1}\) x. Here θ has infinitely many values.
Continue reading "General and Principal Values of cos\(^{1}\) x  Inverse Circular Functions"
Earlier we have seen about linear equation in two variables and an overview of solution of linear equation in two variables. From this topic on wards, we
Continue reading "Method of Elimination  Systems of Equations with Elimination"
Earlier we have studied about the linear equations in one variable. We know that in linear equations in one variable, only one variable is present whose value we need to find out by doing calculations
Continue reading "Solution of a Linear Equation in Two Variables Method of Substitution, Elimi..."
Comparison between Simple Interest and Compound Interest for the same principal amount. Interest is of two kinds – Simple Interest and Compound Interest.
Continue reading "Comparison between Simple Interest and Compound Interest  Solved Examples"
Practice the questions given in the Worksheet on Compound Interest as Repeated Simple Interest. 1. Find the amount and compound interest for $2000 lent for 2 years at 2% rate of interest p.a.
Continue reading "Worksheet on Compound Interest as Repeated Simple Interest  Answers"
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