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Trigonometry
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, Sin 𝛳 = Cos ( 90⁰ - 𝛳 ) Cos 𝛳 = Sin ( 90⁰ - 𝛳 ) tan 𝛳 = cot ( 90⁰ - 𝛳
Algebra
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 Binomial: An Algebraic expression that contains only two terms is called a binomial. Examples: x + y, 4a - 3b , l² -7m Trinomial: An Algebraic expression that contains only three ter
Pythagoras Theorem
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: ∠ B = 90⁰ , AB = 18 cm , BC = 24 cm. By Pythagoras Theorem, AC² = BC² + AB² =18² + 24 ² = 324 + 576 AC² = 900 Th
Angles
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 rays forming a straight line, the angle thus formed is a straight angle and its measure is 180⁰ Reflex angle: An angle whose measure is more than 180⁰ but less than 360⁰ is called a reflex angle. Complete angle: An angle whose measure is 360⁰ is called a complete angle.
Theory of Sets
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. Infinite set: A set is said to be an infinite set if the number of elements in a set is infinite. The cardinal number of a infinite set is not a finite number. Sin