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Cosecant Formula
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What are Cosine Formulas?

Last Updated : 19 Dec, 2023
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Trigonometry is a discipline of mathematics that studies the relationships between the lengths of the sides and angles of a right-angled triangle. Trigonometric functions, also known as goniometric functions, angle functions, or circular functions, are functions that establish the relationship between an angle to the ratio of two of the sides of a right-angled triangle. The six main trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant. Trigonometric angles are the Angles defined by the ratios of trigonometric functions. Trigonometric angles represent trigonometric functions. The value of the angle can be anywhere between 0-360°.

Right Angle Triangle
 

As given in the above figure in a right-angled triangle:

  • Hypotenuse: The side opposite to the right angle is the hypotenuse, It is the longest side in a right-angled triangle and opposite to the 90° angle.
  • Base: The side on which angle C lies is known as the base.
  • Perpendicular: It is the side opposite to angle C in consideration.

Trigonometric Ratios Definition

Trigonometry has 6 basic trigonometric ratios also called trigonometric functions, they are sine, cosine, tangent, cosecant, secant, and cotangent. Now let’s look into the trigonometric functions. The six trigonometric functions are as follows,

  • sine: the ratio of perpendicular and hypotenuse is defined as sine and It is represented as sin θ
  • cosine: the ratio of base and hypotenuse is defined as cosine and it is represented as cos θ
  • tangent: the ratio of sine and cosine of an angle is defined as a tangent. Thus the definition of tangent comes out to be the ratio of perpendicular and base and is represented as tan θ.
  • cosecant: It is the reciprocal of sin θ and is represented as cosec θ.
  • secant: It is the reciprocal of cos θ and is represented as sec θ.
  • cotangent: It is the reciprocal of tan θ and is represented as cot θ.

According to the above image, Trigonometric Ratios are

  • sin θ = Perpendicular/Hypotenuse = AB/AC
  • cos θ = Base/Hypotenuse = BC/AC
  • tan θ = Perpendicular/Base = AB/BC
  • cosec θ = Hypotenuse/Perpendicular = AC/AB
  • sec θ = Hypotenuse/Base = AC/BC
  • cot θ = Base/Perpendicular = BC/AB

Formulas and Identities for Cosine

There are various different identities in trigonometry, some of these identities for cosine trigonometric ratio are discussed as follows:

Reciprocal Identities

  • sin θ = 1/ cosec θ
  • cosec θ = 1/ sin θ
     
  • cos θ = 1/ sec θ 
  • sec θ = 1 / cos θ
     
  • cot θ = 1 / tan θ
  • tan θ = 1 / cot θ
     
  • cot θ = cos θ / sin θ
  • tan θ = sin θ / cos θ
     
  • tan θ.cot θ = 1

Complementary Angles Identities 

Pair of angles whose sum is equal to 90° are called complementary angles and the identities of Complementary angles are:

  • sin (90° - θ) = cos θ
  • cos (90° - θ) = sin θ
  • tan (90° - θ) = cot θ
  • cot (90° - θ) = tan θ
  • sec (90° - θ) = cosec θ
  • cosec (90° - θ) = sec θ

Supplementary Angles Identities

Pair of angles whose sum is equal to 180° are called supplementary angles and the identities of supplementary angles are:

  • sin (180° - θ) = sin θ
  • cos (180° - θ) = - cos θ
  • tan (180° - θ) = - tan θ
  • cot (180° - θ) = - cot θ
  • sec (180° - θ) = - sec θ
  • cosec (180° - θ) = - cosec θ

Cosine Formulas Using Pythagorean Identity

One of the trigonometric identities between sin and cos. It represents  sin2x + cos2x = 1

 sin2x + cos2x = 1

Now Subtracting sin2x from both sides,

cos2x = 1 - sin2x

now square both sides

cos x = ± √(1 - sin2x)

Cosine Formulas with Sum/Difference Formulas

There are sum/difference formulas for every trigonometric function that deal with the sum of angles (x + y) and the difference of angles (x - y). 

Formulas of cosine function with sum difference formulaes are,

cos(x + y) = cos (x) cos(y) – sin (x) sin (y)

cos (x – y) = cos (x) cos (y) + sin (x) sin (y)

Formulas for Law of Cosines

This law is used to find the missing sides/angles in a non-right angled triangle. Assume a triangle ABC in which AB = c, BC = a, and CA = b. 

The cosine formulas  are,

cos A = (b2 + c2 - a2)/(2bc)

cos B = (c2 + a2 - b2)/(2ac)

cos C = (a2 + b2 - c2)/(2ab)

Learn more about, Law of Cosine Formula

Double Angle Formula of Cosine

 In trigonometry while dealing with 2 times the angle. There are multiple sorts of double-angle formulas of cosine and from that, we use one of the following while solving the problem depending on the available information. 

cos 2x = cos2(x) – sin2(x)

cos 2x = 2 cos2(x) − 1  

cos 2x = 1 – 2 sin2(x)

cos 2x = [(1 - tan2x)/(1 + tan2x)]

Half Angle Formula of Cosine

Half angle formula for the cosine is similar to the double angle formula but 2(Angle) is changed to (Angle). The half-angle formula for the cosie is,

cos (x/2) =± √[ (1 + cos x) / 2]

Triple Angle Formula of Cosine

The triple angle formula for the cosine is,

cos 3x = 4cos3x - 3cosx 

Read More,

  • Trigonometric Identities
  • Trigonometric Table

Sample Problems on Cosine Formulas

Problem 1: If sin a = 3/5 and a is in the first quadrant, find the value of cos a.

Solution:

Using one of the cosine formulas,

cos a = ± √(1 - sin2a)

Since a is in the first quadrant, cos a is positive. Thus,

cos a = √(1 - sin2a)

Substitute sin a = 3/5 here,

cos a = √(1 - (3/5)2)  

⇒ cos a = √(1 - 9/25)

⇒ cos a =√ (16/25)

Thus, cos a = 4/5

Problem 2: If sin (90 - A) = 2/3, then find the value of cos A.

Solution:

Using one of the cosine formulas,

cos A = sin (90 - A)

given that sin (90 - A) = 2/3. Hence,

cos A = 2/3

The value of cos A is 2/3.

Problem 3: In a triangle ABC, AB = c, BC = a, and CA = b. Also, a = 50 units, b = 60 units, and c = 30 units. Find cos A.

Solution:

By Using the cosine formula of law of cosines,

cos A = (b2 + c2 - a2) / (2bc)

⇒ cos A = (602 + 302 - 502) / (2 · 60 · 30)

⇒ cos A = (3600 + 900 - 2500) / 3600

⇒ cos A = 2000 / 3600

Thus, cos A = 5/9

Problem 4: If cos A = 4/5, cos B = 12/13, find the value of cos (A+B)?

Solution: 

Here given cos A = 4/5, cos B = 12/13

since A and B both lie in 4th quadrant and in 4th quadrant Sin A and Sin B will be negative.

therefore, 

sin A  = - √(1 - cos2 A)

⇒ sin A =  √{1 - (4/5)2 }

⇒ sin A =  - √(1 - 16/25)

⇒ sin A =  -3/5

and sin B = - √(1 - cos2 B)

⇒ sin B =  - √{1 - (12/13)2}

⇒ sin B =  -5/13

Now, as per the formula 

cos(A + B) = cos (A) cos(B) – sin (A) sin (B)

⇒ cos(A + B) = 4/5 × 12/13 - (-3/5)(-5/13)

⇒ cos(A + B) = 48/65 - 15/65

⇒ cos(A + B) = 33/65

Problem 5: Prove that cos4x = 1- 8sin2xcos2x.

Solution: 

Given that 

LHS = cos4x

⇒ LHS = cos2(2x) 

⇒ LHS = cos 2x     [As cos 2x = 1 – 2 sin2(x)]

⇒ LHS = 1 – 2 sin2  2(x)

⇒ LHS = 1 - 2 (sin2x)2

⇒ LHS = 1 - 2(2sinx cosx)2

⇒ LHS =  1 -  8sin2xcos2x 

⇒ LHS =  RHS 

[Hence Proved]


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    Surface Area of Sphere | Formula, Derivation and Solved Examples
    A sphere is a three-dimensional object with all points on its surface equidistant from its center, giving it a perfectly round shape. The surface area of a sphere is the total area that covers its outer surface.To calculate the surface area of a sphere with radius r, we use the formula:Surface Area
    8 min read
    Surface Area of a Square Pyramid
    Pyramid is a three-dimensional geometric structure with a polygonal base and triangular faces equal to the number of sides in the base. The triangular faces or lateral surfaces of a pyramid meet at a single point known as the apex or the vertex. Surface Area of a Square Pyramid In a pyramid, the bas
    8 min read
    Volume of a Pyramid Formula
    Pyramid is a three-dimensional shape whose base is a polygon, and all its triangular faces join at a common point called the apex. The pyramids of Egypt are real-life examples of pyramids. Volume of a pyramid is the space occupied by that pyramid and is calculated by the formula, V = 1/3×(Area of Ba
    9 min read
    Frustum of Cone
    Frustum of a cone is a special shape that is formed when we cut the cone with a plane parallel to its base. The cone is a three-dimensional shape having a circular base and a vertex. So the frustum of a cone is a solid volume that is formed by removing a part of the cone with a plane parallel to cir
    10 min read
    Volume of a Square Pyramid Formula
    A pyramid is a three-dimensional polyhedron with a polygonal base and three or more triangle-shaped faces that meet above the base. The faces are the triangle sides, while the apex is the point above the base. The base is connected to the peak to form a pyramid. When the pyramid's base is in the sha
    8 min read
    Surface Area of a Prism
    Surface Area of a Prism: In mathematics, a prism is an essential member of the polyhedron family and is defined as a three-dimensional shape having two identical polygons facing each other that are connected by rectangular or parallelogram faces laterally. The identical polygons can be triangles, sq
    13 min read
    Frustum of a Regular Pyramid Formula
    A Pyramid is a Mathematical figure having three or four triangular faces as sides and a flat polygonal base which can be triangular, square or rectangular, etc. The side triangular faces are called Lateral faces. The common meeting point of all the triangular faces is called the apex. For a given py
    6 min read

    Algebra

    Basic Math Formulas
    Mathematics is divided into various branches according to the way of calculation involved and the topics covered by them. All the branches have various formulas that are used for solving various mathematical problems. The branches include geometry, algebra, arithmetic, percentage, exponential, etc.T
    12 min read
    Algebra Formulas - List of all Algebra Formulas
    Algebra formulas are mathematical expressions that help solve problems involving variables and constants. They often represent relationships between quantities and can be used to simplify calculations. This article provides a comprehensive overview of all algebra formulas taught from Class 9 through
    10 min read
    Polynomial Formula
    The polynomial Formula gives the standard form of polynomial expressions. It specifies the arrangement of algebraic expressions according to their increasing or decreasing power of variables. The General Formula of a Polynomial:f(x) = an​xn + an−1​xn−1 + ⋯ + a1​x + a0​Where,an​, an−1​, …, a1​, a0​ a
    5 min read
    Factorization of Polynomial
    Factorization in mathematics refers to the process of expressing a number or an algebraic expression as a product of simpler factors. For example, the factors of 12 are 1, 2, 3, 4, 6, and 12, and we can express 12 as 12 = 1 × 12, 2 × 6, or 4 × 3.Similarly, factorization of polynomials involves expre
    10 min read
    What is Factoring Trinomials Formula?
    A Trinomial is a polynomial with three terms. Examples of Trinomial are x+y+z, x2+2x+2, x+y-1 etc. A Trinomial can be of two types. They are Perfect Square Trinomial and Non-Perfect Square Trinomial. Factoring a polynomial is nothing but writing the expression polynomial as a product of two or more
    4 min read
    a2 - b2 Formula
    a2 - b2 formula in Algebra is the basic formula in mathematics used to solve various algebraic problems. a2 - b2 formula is also called the difference of squares formula, as this formula helps us to find the difference between two squares without actually calculating the squares. The image added bel
    6 min read
    Difference of Cubes
    Difference of Cubes is the formula in mathematics that is used to simplify the difference between two cubes. This formula is used to solve the difference of cubes without actually finding the cubes. This formula factorizes the difference of a cube and changes it into other forms. The difference of c
    6 min read
    Discriminant Formula in Quadratic Equations
    Algebra can be defined as the branch of mathematics which deals with the study, alteration, and analysis of various mathematical symbols. It is the study of unknown quantities, which are often depicted with the help of variables in mathematics. Algebra has a plethora of formulas and identities for t
    5 min read
    Sum of Arithmetic Sequence Formula
    An arithmetic sequence is a number series in which each subsequent term is the sum of its preceding term and a constant integer. This constant number is referred to as the common difference. As a result, the differences between every two successive terms in an arithmetic series are the same.If the f
    5 min read
    Function Notation Formula
    A function is a type of operator that takes an input variable and provides a result. When one quantity is dependent on another, a function is created. An interesting property of functions is that each input corresponds to a single output. In other words, such an operator between two sets, say set A
    4 min read
    Binomial Distribution in Probability
    Binomial Distribution is a probability distribution used to model the number of successes in a fixed number of independent trials, where each trial has only two possible outcomes: success or failure. This distribution is useful for calculating the probability of a specific number of successes in sce
    14 min read
    Binomial Expansion Formulas
    Binomial expansion formula is a formula that is used to solve binomial expressions. A binomial is an algebraic expression with two terms. For example, x + y, x - a, etc are binomials. In this article, we have covered the Binomial Expansion definition, formulas, and others in detail.Table of ContentB
    8 min read
    Binomial Theorem
    Binomial theorem is a fundamental principle in algebra that describes the algebraic expansion of powers of a binomial. According to this theorem, the expression (a + b)n where a and b are any numbers and n is a non-negative integer. It can be expanded into the sum of terms involving powers of a and
    15+ min read
    FOIL Method
    FOIL formula is used to perform multiplication between two binomials. A binomial is a polynomial with only two terms. Example: x+3, x2+4, 5x2+3x. A binomial is a 2 term algebraic expression that includes constants, variables, exponents and coefficients. Each letter in the FOIL represent steps to mul
    2 min read
    Exponential Decay Formula
    Exponential Decay Formula: A quantity is said to be in exponential decay if it decreases at a rate proportional to its current value. In exponential decay, a quantity drops slowly at first before rapidly decreasing. The exponential decay formula is used to calculate population decay (depreciation),
    7 min read
    Factorial Formula
    The factorial is one of the most fundamental mathematical operations in combinatorics, algebra, and number theory. Represented by an exclamation mark (!), the factorial of a non-negative integer n, denoted as n!, is the product of all positive integers less than or equal to n. It plays a crucial rol
    8 min read
    Combinations Formula with Examples
    Combinations are way of selecting items from a collection of items. Different groups that can be formed by choosing r things from a given set of n different things, ignoring their order of arrangement, are called combinations of n things taken r at a time.The number of all such combinations is calcu
    6 min read
    Fourier Series Formula
    Fourier Series is a sum of sine and cosine waves that represents a periodic function. Each wave in the sum, or harmonic, has a frequency that is an integral multiple of the periodic function’s fundamental frequency. Even though a Fourier series can include infinitely many harmonics, using just a few
    15 min read
    Maclaurin series
    Prerequisite - Taylor theorem and Taylor series We know that formula for expansion of Taylor series is written as: f(x)=f(a)+\sum_{n=1}^{\infty}\frac{f^n(a)}{n!}(x-a)^n Now if we put a=0 in this formula we will get the formula for expansion of Maclaurin series. T hus Maclaurin series expansion can b
    2 min read

    Coordinate Geometry

    Mid Point Formula in Coordinate Geometry
    Mid point formula in coordinate geometry provides a way to find the mid point of a line segment when the coordinates of the starting and ending points ( i.e. (x1, y1) and (x2, y2) )of the line segment is known. The mid point divides the line in two equal halves i.e the ratio of the sections of the l
    6 min read
    Equation of a Straight Line | Forms, Examples and Practice Questions
    The equation of a line describes the relationship between the x-coordinates and y-coordinates of all points that lie on the line. It provides a way to mathematically represent that straight path.In general, the equation of a straight line can be written in several forms, depending on the information
    10 min read
    Equation of a Circle
    A circle is a geometric shape described as the set of all points in a plane that are equidistant from a fixed point called the center. The distance from the center to any point on the circle is called the radius. Some key components of the circle are:Center: The fixed point in the middle of the circ
    14 min read
    Ellipse Formula
    An ellipse is a set of points such that the sum of the distances from any point on the ellipse to two fixed points (foci) is constant. In this article, we will learn about the ellipse definition, Ellipse formulas, and others in detail.Table of ContentWhat is Ellipse?What is Ellipse Formula?Major and
    8 min read

    Trigonometry

    30-60-90 Formula
    A 30-60-90 triangle is a special type of right triangle with one angle measuring 30°, another 60°, and the third angle (the right angle) measuring 90°. The 30-60-90 triangle is called a special right triangle as the angles of this triangle are in a unique ratio of 1:2:3. Here, a right triangle means
    7 min read
    Cofunction Formulas
    A trigonometric cofunction is defined as expressing a trigonometric angle ratio in terms of the other. It illustrates how sine, cosine, tangent, cotangent, secant, and cosecant relate to each other. The cofunction of an angle's complement is equal to that angle's trigonometric function. For example,
    7 min read
    What is Cos Square theta Formula?
    The equations that relate the different trigonometric functions for any variable are known as trigonometric identities. These trigonometric identities help us to relate various trigonometric formulas and relationships with different angles. They are sine, cosine, tangent, cotangent, sec, and cosec.
    3 min read
    What are Cosine Formulas?
    Trigonometry is a discipline of mathematics that studies the relationships between the lengths of the sides and angles of a right-angled triangle. Trigonometric functions, also known as goniometric functions, angle functions, or circular functions, are functions that establish the relationship betwe
    8 min read
    Cosecant Formula
    Cosecant is one of the six basic trigonometric ratios and its formula is cosecant(θ) = hypotenuse/opposite, it is also represented as, csc(θ). It is the inverse(reciprocal) ratio of the sine function and is the ratio of the Hypotenus and Opposite sides in a right-angle triangle. In this article, we
    4 min read
    Cotangent Formula
    Trigonometry is an important branch of mathematics that deals with the relation between the lengths of sides and angles of a right-angled triangle. Sine, Cosine, tangent, cosecant, secant, and cotangent are the six trigonometric ratios or functions. Where a trigonometric ratio is depicted as the rat
    7 min read
    Tangent Formulas
    Tangent Function is among the six basic trigonometric functions and is calculated by taking the ratio of the perpendicular side and the hypotenuse side of the right-angle triangle.In this article, we will learn about Trigonometric ratios, Tangent formulas, related examples, and others in detail.Tabl
    8 min read
    Cot Half Angle Formula
    Trigonometry is a branch of mathematics that uses trigonometric ratios to determine the angles and incomplete sides of a triangle. The trigonometric ratios such as sine, cosine, tangent, cotangent, secant, and cosecant are used to investigate this branch of mathematics. It's the study of how the sid
    6 min read
    2cosA cosB Formula
    The identity 2 cos A cos B = cos(A + B) + cos(A – B) is one of the important product-to-sum formulas in trigonometry. This identity is used to convert a product of cosine functions into a sum of cosines, which can simplify the process of solving trigonometric equations, evaluating integrals, and per
    7 min read
    Multiple Angle Formulas
    Trigonometry is one of the important topics in mathematics that is used in various fields. The trigonometric formulae are applied and used in various formulae, derivations, etc. This article is about the multiple angle formulae in trigonometry where we find sine, cosine, and tangent for multiple ang
    5 min read
    Double Angle Formula for Cosine
    Double angle formula for cosine is a trigonometric identity that expresses cos⁡(2θ) in terms of cos⁡(θ) and sin⁡(θ) the double angle formula for cosine is, cos 2θ = cos2θ - sin2θ. The formula is particularly useful in simplifying trigonometric expressions and solving equations involving trigonometri
    5 min read
    Inverse Trigonometric Functions | Definition, Formula, Types and Examples
    Inverse trigonometric functions are the inverse functions of basic trigonometric functions. In mathematics, inverse trigonometric functions are also known as arcus functions or anti-trigonometric functions. The inverse trigonometric functions are the inverse functions of basic trigonometric function
    11 min read

    Complex Number

    Complex Number Formula
    The sum of a real number and an imaginary number is defined as a complex number, and the numbers that are not real numbers are called imaginary numbers. The number can be written in the form of b+ic, where b and c are real numbers ic is an imaginary number, and ” i” is an imaginary part which is cal
    13 min read
    Absolute Value of a Complex Number
    The absolute value (also called the modulus) of a complex number z = a + bi is its distance from the origin in the complex plane. The absolute value tells you how far a number is from zero, regardless of its direction (positive or negative).It is denoted as ∣z∣ and is given by the formula:|z| = \sqr
    7 min read
    Complex Number Power Formula
    Complex Numbers are numbers that can be written as a + ib, where a and b are real numbers and i (iota) is the imaginary component and its value is √(-1), and are often represented in rectangle or standard form. 10 + 5i, for example, is a complex number in which 10 represents the real component and 5
    6 min read
    DeMoivre's Theorem
    De Moivre's theorem is one of the fundamental theorem of complex numbers which is used to solve various problems of complex numbers. This theorem is also widely used for solving trigonometric functions of multiple angles. DeMoivre’s Theorem is also called “De Moivre’s Identity” and “De Moivre’s Form
    6 min read
    Covariance Matrix
    A Covariance Matrix is a type of matrix used to describe the covariance values between two items in a random vector. It is also known as the variance-covariance matrix because the variance of each element is represented along the matrix’s major diagonal and the covariance is represented among the no
    10 min read
    Determinant of Matrix with Solved Examples
    The determinant of a matrix is a scalar value that can be calculated for a square matrix (a matrix with the same number of rows and columns). It serves as a scaling factor that is used for the transformation of a matrix.It is a single numerical value that plays a key role in various matrix operation
    15+ min read

    Calculus

    Limit Formula
    Limits help us comprehend how functions behave as their inputs approach certain values. Think of a limit as the destination that a function aims to reach as the input gets closer and closer to a specific point.In this article, we will explore the essential limit formulas that form the backbone of ca
    7 min read
    Average and Instantaneous Rate of Change
    The average rate of change represents the total change in one variable in relation to the total change of another variable. Instantaneous rate of change, or derivative, measures the specific rate of change of one variable in relation to a specific, infinitesimally small change in the other variable.
    8 min read
    Calculus | Differential and Integral Calculus
    Calculus was founded by Newton and Leibniz. Calculus is a branch of mathematics that helps us study change. It is used to understand how things change over time or how quantities grow, shrink, or accumulate. There are two main parts of calculus:Differential Calculus: It helps us calculate the rate o
    4 min read
    Total Derivative
    Total Derivative of a function measures how that function changes as all of its input variables change. For function f at a point is an approximation near the point of the function w.r.t. (with respect to) its arguments (variables).It is an approximation of the actual change in the function and is u
    5 min read
    Difference Quotient Formula
    The Difference Quotient Formula is a part of the definition of a function derivative. One can get derivative of a function by applying Limit h tends to zero i.e., h ⇢ 0 on difference quotient function. The difference quotient formula gives the slope of the secant line. A secant line is a line that p
    5 min read
    Chain Rule: Theorem, Formula and Solved Examples
    The Chain Rule is a way to find the derivative of composite functions. It is one of the basic rules used in mathematics for solving differential equations. It helps us to find the derivative of composite functions such as (3x2 + 1)4, (sin 4x), e3x, (ln x)2, and others. Only the derivatives of compos
    8 min read
    Implicit Differentiation
    Implicit Differentiation is the process of differentiation in which we differentiate the implicit function without converting it into an explicit function. For example, we need to find the slope of a circle with an origin at 0 and a radius r. Its equation is given as x2 + y2 = r2. Now, to find the s
    5 min read
    Antiderivative: Integration as Inverse Process of Differentiation
    An antiderivative is a function that reverses the process of differentiation. It is also known as the indefinite integral. If F(x) is the antiderivative of f(x), it means that:d/dx[F(x)] = f(x)In other words, F(x) is a function whose derivative is f(x).Antiderivatives include a family of functions t
    7 min read
    Integration Formulas
    Integration Formulas are the basic formulas used to solve various integral problems. They are used to find the integration of algebraic expressions, trigonometric ratios, inverse trigonometric functions, and logarithmic and exponential functions. These integration formulas are beneficial for finding
    10 min read
    Integration by Parts
    Integration by Parts or Partial Integration, is a technique used in calculus to evaluate the integral of a product of two functions. The formula for partial integration is given by:∫ u dv = uv - ∫ v duWhere u and v are differentiable functions of x. This formula allows us to simplify the integral of
    9 min read
    Integration by Substitution Formula
    The process of finding the anti-derivative of a function is the inverse process of differentiation i.e. finding integral is the inverse process of differentiation. Integration can be used to find the area or volume of a function with or without certain limits or boundaries It is shown as∫g(x)dx = G(
    5 min read
    Definite Integral | Definition, Formula & How to Calculate
    A definite integral is an integral that calculates a fixed value for the area under a curve between two specified limits. The resulting value represents the sum of all infinitesimal quantities within these boundaries. i.e. if we integrate any function within a fixed interval it is called a Definite
    8 min read
    Area Under Curve
    Area Under Curve is area enclosed by curve and the coordinate axes, it is calculated by taking very small rectangles and then taking their sum if we take infinitely small rectangles then their sum is calculated by taking the limit of the function so formed.For a given function f(x) defined in the in
    11 min read
    Differentiation and Integration Formula
    Differentiation and Integration are two mathematical operations used to find change in a function or a quantity with respect to another quantity instantaneously and over a period, respectively. Differentiation is an instantaneous rate of change, and it breaks down the function for that instant with
    11 min read
    Differential Equations
    A differential equation is a mathematical equation that relates a function with its derivatives. Differential Equations come into play in a variety of applications such as Physics, Chemistry, Biology, Economics, etc. Differential equations allow us to predict the future behavior of systems by captur
    12 min read
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