Combination formula: Applying the combination formula
You studied this formula while touching the topic of probability, right? When you select some specific objects out of total specific objects, the combination formula applies. In combination, you make a selection without making an arrangement.
The combination formula can be given as C (n, r) = n! / r! (n-r)!, where n is the total number of objects and r is number of selected objects out of n total objects. Let us work together on a problem to apply the formula.
Problem 1: Consider a situation in which 5 kids are playing in a play ground. Suddenly, it starts raining and 3 kids are called home by their parents. How can those 3 kids be selected?
Solution 1: Here, n = 5 and r = 3.
Applying the combination formula, we can derive that
C (5, 3) = 5! / 3! (5-3)! => C (5, 3) = 5! / 3! 2! => C (5, 3) = 10.
Trigonometry formulas: Learning the trigonometry formulas
In trigonometry, you study about triangles, their angles, and their sides. Thus, you come across various properties of triangles and their types. Let us see some basic trigonometry formulas at a glance.
Sin = Perpendicular / base
Cos = Base / hypotenuse
Tan = Perpendicular/ base
How do you identify the sides known as perpendicular, base, and hypotenuse? It’s easy.
In a right angled triangle in which hypotenuse is the side opposite to the right angle, perpendicular is the adjacent vertical side, and base is the adjacent horizontal side.
Apart from these basic formulas, you can also grasp the concept of angle of elevation. An angle of elevation is the angle formed when an observer sees an object above his own height.
In addition, there is a basic triangle formula that you must remember. The formula is given by
A = ½ * base * height, where base and height are the respective dimensions of a triangle. Let us solve a problem by applying the formula.
Problem 2: Find out the area of a triangle with base 4 units and height 10 units.
Solution 2: Area = ½ * 4 * 10 = 20 sq. units.
Circle formulas: Utilizing the circle formulas
Circle formulas apply on numerous geometry problems and on real-life situations, as well. For instance, if you know the process of finding the area of a circle, you can easily find out the fencing area. Therefore, let us start by absorbing some fundamental circle formulas.
Area of a circle = pi * r * r
Circumference of a circle = 2 * pi * r
Let us get together to work on a problem.
Problem 3: Calculate the radius of a circle that has a circumference of 44 units.
Solution 3: Here, Circumference = 44 …….. (1)
Circumference of a circle = 2. pi. r……….. (2)
Equating (1) and (2), we get:
44 = 2 * pi * r => r = 7 units.