Mathematics

 Trigonometry is the one of the branches of mathematics which means the measurement of triangle. Trigonometric Ratios:   The side that is opposite to the right angle is called the Hypotenuse.  This is the longest in a right triangle. The side that is opposite to the angle 𝛳 is called the opposite side. The side  that runs alongside the angle  𝛳 and which is not the Hypotenuse is called the Adjacent side. Let 𝛳 be an acute angle  of a right triangle. Then the six trigonometric Ratios of 𝛳 and the trigonometric table are as follows,           Example:           Trigonometric Ratios of Complementary Angles  Let 𝛳 be an acute angle  of a right triang le. Then we have the following identities for the trigonometric rat ios of  Complementary angles,                          ...

The mathematical term "Algebra" was derived from the Arabic word 'al-jabr'  Indian mathematicians like  Aryabhatta , Bhrahmagupta, Mahavir, Bhaskara Ⅱ, Sridhara have contribute a lot to this branch of mathematics.         The Greek mathematician, Diophantus of Alexandria  had developed this branch to a greater extent. Hence he is called as "The father of Algebra"             Basic concepts of Polynomial: Monomial:                    An Algebraic expression that contains only one term is called a monomial.                        Examples:                                    2x², 3ab,81xyz                                ...

 Pythagoras theorem is the important one which gives the relation between the three sides of the right angled triangle.        This theorem was discoveredby a famous mathematician"PYTHAGORAS"   Statement:        In a right angled triangle the square of the hypotenuse is equal to the sum of the squares of the  other two sides.                        Let us consider ∆ ABC  with ∠C = 90⁰ ,      BC = a , CA = b and AB = c , then                a² + b² = c²         Application:    In   ∆ ABC ,    ∠ B =   90⁰ ,  AB = 18 cm and BC = 24 cm. Calculate the length of AC.       Solution:                       Given:            ...

     Two rays starting from a common point from an angle. Types of angles: Acute angle:          An angle whose measure is greater than  0⁰ but less than 90⁰ is called an acute angle.                   Examples:                            15⁰ , 30⁰.      Right angle:              An angle whose measure is 90⁰ is called a right angle.   Obtuse angle:             An angle whose is greater than 90⁰ and less than 180⁰ is called an obtuse angle.                                     Examples:   100⁰ , 110⁰ , 140⁰  Straight angle:             When the rays of an angle are opposite ...

A set is  a collection of well  defined objects. The objects of a set are called elements or members of the set. A set is denoted by the capital letters.   Example:            The collection of jewels    in your home. Cardinal Number:             The number of elements in a set "A"  is called the cardinal number of a set and it is denoted by n(A). Different kinds of sets: The empty set:         A set which containing no elements is called the empty set  or null set or void set.           The cardinal number of the empty set is zero.     Finite set:                If the number of elements in a set is zero or finite,then the set is called a finite set.                   The cardinal number of a finite set is finite. ...