MATHEMATICS
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Pythagoras’ theorem is stated as : The sum of the areas of the two squares on the perpendicular(p) and base(b) of a right-angle triangle is equal to the area of the square on the hypotenuse(h). i.e. p2 + b2 = h2 READ MORE...

A right-angle triangle is a triangle in which one of the angles measures 90°. Right-angled triangles have wide applications in mathematics and physics and as such, it became convenient to have specific names for their sides so that the problem statement in mathematics can be easily described. One of the angles measures 90°. If we denote one of the remaining two angles by θ, then the third angle would be 90°- θ. With reference to the angle θ, we have the below definitions: The side opposite the right angle(90°) is called the hypotenuse. The hypotenuse is also the longest side in a right-angle triangle. The side opposite to the angle θ is called perpendicular. The side containing both the right angle and θ […] READ MORE...

The trigonometric functions can be described on an x-y coordinate plane (Euclidean plane) using a circle of radius 1 unit and cutting a sector that subtends an angle θ at the centre. Refer to the diagram below for details. READ MORE...

By definition, L (length of arc) = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × Circumference (arc length is proportional to angle, one complete arc subtends 360° at center) Also, Circumference = 2 ? r Hence, L = ( \dfrac { \mathrm{θ_{deg} } } {360} ) × 2 ? r      - - - - - (i) Now, again by definition,  θrad   = ( \dfrac{ \mathrm{L} }{ r } )    (radian is ration of arc length to radius) So, L = r × θrad    - - - - - (ii) From (i) & (ii), we have  r × θrad= ( \dfrac { \mathrm{θ_{deg} } } {360} ) × 2 ? r Or, θrad = θdeg  × […] READ MORE...

A number not divisible by 2 is called an odd number. Any number whose unit digit(last digit) is either 1,3,5,7 or 9 is an odd number. The set of all odd numbers is represented as Odd numbers = { 2n+1: n ∈  Z } where Z is the set of all integers. When an even number is subtracted from an odd number, it results in an odd number. When two odd numbers are subtracted, it results in an even number. READ MORE...

A number divisible by 2 is called an even number. All numbers whose unit digit(last digit) is either 0,2,4,6 or 8 is an even numbers. The set of all even numbers is represented as follows: Even numbers = { 2n: n ∈  Z } where Z is the set of all integers. Zero is an even number. The addition or subtraction of two even numbers always results in an Even number When a number (even or odd) is multiplied by an even number, it results in an Even Number. When an even number is subtracted from an odd number or vice-versa, it results in an odd number. ( 7 - 4 = 3 , 8 - 3 = 5 ...) […] READ MORE...

The cartesian product of two sets A and B is defined as a set formed by all the possible ordered pairs of elements from A and B, such that the first element comes from set A and the second element comes from set B. The cartesian product is denoted as A × B. ​Let a and b represent arbitrary elements from set A and set B respectively. So, a ∈ A and b ∈ B. Then A × B = { (a,b) | a ∈ A, b ∈ B }. Remember ☞ ​If A has m elements and B has n elements then their cartesian product will have m × n elements.If n(A) = m and n(B)=n ,  then n(A […] READ MORE...