Introduction The notion of trigonometry was developed by the Greek mathematician Hipparchus, while the name trigonometry is a 16th-century Latin derivative. Trigonometry is one of the most important branches of mathematics. The name "trigonometry" is made up of the phrases "Trigonon" and "Metron, " which denote a triangle and a measure, respectively. It is the study of the relationship between the sides and angles of a right-angled triangle. The ratio of the hypotenuse's length to the neighbouring side's (base) length is known as the sec of an angle in a right triangle. The angle 0° for sec 0 degrees is ... Read More

Introduction In any business or research activity, a large number of data is produced, which becomes difficult to analyse. In this direction, a statistical process, sampling, is useful to analyse the entire population. However, in doing so, some error arises due to various reasons. For accurate data analysis, one must know about sampling and the various types of error associated with it. In this tutorial, we will discuss sampling, sampling errors, a basic formula, properties, and ways to minimize sampling error with solved examples. Sampling In statistics, sampling is defined as the process of selection of specific data from a ... Read More

Introduction Division is the basic arithmetical operation in mathematics. It is the process of distributing things into equal parts. When the dividend is not completely divisible by the divisor it left a number or the value is known as the remainder. In mathematics, in numerous instances, the leftover part or value is known as residues. Sometimes in many calculations residues are neglected or round off to obtain the answer in the whole number. For example, in the decimal number 5.04, the number after the decimal is 4. It represents remainder or residue. Sometimes to give only a whole number answer, ... Read More

Introduction The term Reciprocal means inversely related. In fraction, the term Reciprocal is taking the inverse, that is the place of numerator and denominator exchanges with each other. To check the Reciprocal value is taken the correct, invert and multiply that inverted number with the original number always equal to one. Or if a number is multiplied by another number which is equal to one is reciprocal to each other. Division of fraction is made only by taking the reciprocal or multiplicative inverse. Numbers The term number means a word which represents the count, the measure, the quantity, which is ... Read More

Introduction Sampling techniques refer to the different sampling techniques used to collect different types of samples in statistics. If you need to make statistical inferences about a population, it is almost impossible to collect data from all the units that belong to that group. In these situations, various sampling methods can help you select the correct sample from this population for analysis. In this tutorial, we will discuss random sampling, its type, formulas, and examples. Random sampling Definition Random sampling can be considered as a case of probability sampling. where each and every unit from the population into the ... Read More

Introduction Poisson distributions are frequently used to comprehend various events that take place continuously over a predetermined period of time. The Poisson distribution is a discrete function , therefore the variable can only take values from a list of (possibly infinite) numbers. The Poisson distribution is used in probability and statistics concepts of mathematics. It is a discrete probability distribution used in probability theory and statistics to express the chances of happening that a given number of events will happen within a given time period and regardless of the amount of time that has passed since the last outcome. Definition ... Read More

Introduction You go shopping on a bright sunny day. You chose nice jeans and decided to pay with a credit card. But suddenly you realized that you couldn't remember your PIN. What a tragedy! Now what you can think of is to list all possible combinations to understand your pin. How many combinations are possible? If you list and count all possible combinations, the answer to this question will be difficult. In these situations, the basic principle of counting or the principle of multiplication is useful. Number system A number system is defined as a system of writing to ... Read More

Introduction We need to develop various mathematical models to establish relationships between multiple variables in real life. In this direction, differential equations play an important role. These are applied parts of mathematics and used in calculus. In this tutorial, we will discuss the meaning, order, degree, and types of differential equations with solved examples. Differential Equations Differential equations are mathematical statements containing functions and their derivatives. It describes the relationship between the variables with their rate of change. It is used in engineering, science, biology, finance, etc. The differential equations contain at least one ordinary derivative or partial derivative term. ... Read More

Introduction We studied in the previous classes that the system of two linear equations in two variables namely $\mathrm{a_{1}x\:+\:b_{1}y\:=\:c_{1}\:and\:a_{2}x\:+\:b_{2}y\:=\:c_{2}}$ will have unique solution if $\mathrm{\frac{a_{1}}{b_{1}}\:\neq\:\frac{a_{2}}{b_{2}}\:i.e.\:a_{1}b_{2}\:-\:b_{1}a_{2}\:\neq\:0}$. Thus, $\mathrm{(a_{1}b_{2}\:-\:b_{1}a_{2})}$ is the determining factor for the system of two linear equations. We define $\mathrm{a_{1}b_{2}\:-\:b_{1}a_{2}}$ to be the determinant of the square matrix of order 2. In this tutorial we define the determinant of the square matrix of order 2 and 3 and understand the properties of determinants along with some solved examples. Determinant To every square matrix $\mathrm{A\:=\:[a_{ij}]}$ of order 𝑛, we can associate a real or complex number called ... Read More

Introduction The study of geometric figures using coordinate axes is known as coordinate geometry. Figures like circles, ellipses, polygons, and straight lines can be drawn and scaled on the coordinate axes with ease. Additionally, coordinate geometry facilitates algebraic operations and the study of the properties of geometric figures. Every location on this globe has coordinates that make it simple for us to find them on a map. Our planet's coordinate system is made up of fictitious lines known as latitudes and longitudes. We have the coordinate axes with the horizontal x-axis and the vertical y- axis, which are similar ... Read More