# AI Math Formula

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**About MathCrave AI Math Formula**

MathCrave AI Math Formula tool holds great significance as it simplifies and expedites the process of formulating mathematical equations in engineering. By automatically generating formulas, it reduces the time and effort required for engineers and students to come up with these often complex mathematical expressions.

Moreover, the clear explanations accompanying each formula help users better understand the underlying principles and concepts. This enhances their overall comprehension of engineering mathematics and allows them to apply the formulas effectively in various problem-solving scenarios.

The inclusion of worked examples is particularly valuable as it demonstrates the practical implementation of the formulas. Users can see how the equations are used to solve real-world engineering problems, providing them with a concrete understanding of their usefulness and relevance.

MathCrave AI Math formula generator caters to both basic and advanced engineering mathematics. This versatility is significant as it supports learners at different levels of proficiency, from novice students to experienced engineers. It serves as a valuable resource for education, self-study, and professional applications, offering a wide range of formulas and their explanations.

### Featured Math Formula Calculator to Generate

#### Binomial

Binomial coefficient

Binomial Formula for Positive Integral n

Properties of Binomial Coefficients

Multinominal formula

#### Complex numbers

Complex numbers;

Arithmetic of complex numbers;

Equality of complex numbers;

Polar form of complex numbers;

Absolute value of a complex number;

Multiplication of complex number in polar form;

Division of complex numbers in polar form;

De Moivre’s Theorem

Roots of Complex Numbers;

#### Quadratic equations

Quadratic Equation;

Cubic Equation;

Quartic Equation;

#### Geometric and shapes

Rectangle of Length b and Width a;

Parallelogram of Altitude h and Base b;

Triangle of Altitude h and Base b;

Trapezoid of Altitude h and Parallel Sides a and b;

Regular Polygon of n Sides Each of Length b;

Circle of Radius r;

Sector of Circle of Radius r;

Radius of Circle Inscribed in a Triangle of Sides a, b, c;

Radius of Circle Circumscribing a Triangle of Sides a, b, c;

Regular Polygon of n Sides Inscribed in Circle of Radius r;

Regular Polygon of n Sides Circumscribing a Circle of Radius r;

Segment of Circle of Radius r;

Ellipse of Semi-major Axis a and Semi-minor Axis b;

Segment of a Parabola;

Rectangular Parallelepiped of Length a, Height b, Width c;

Parallelepiped of Cross-sectional Area A and Height h;

Sphere of Radius r;

Right Circular Cylinder of Radius r and Height h;

Circular Cylinder of Radius r and Slant Height l;

Cylinder of Cross-sectional Area A and Slant Height l;

Right Circular Cone of Radius r and Height h;

Pyramid of Base Area A and Height h;

Spherical Cap of Radius r and Height h;

Frustum of Right Circular Cone of Radii a, b and Height h;

Spherical Triangle of Angles A, B, C on Sphere of Radius r;

Torus of Inner Radius a and Outer Radius b;

Ellipsoid of Semi-axes a, b, c;

Paraboloid of Revolution;

Distance d Between Two Points P1(x1, y1) and P2(x2, y2)

Slope m of Line Joining Two Points P1(x1, y1) and P2(x2, y2)

Equation of Line Joining Two Points P1(x1, y1) and P2(x2, y2)

Equation of Line in Terms of x Intercept a ≠ 0 and y Intercept b ≠ 0

Normal Form for Equation of Line

General Equation of Line

Angle ψ Between Two Lines Having Slopes m1 and m2

Area of Triangle with Vertices at (x1, y1), (x2, y2), (x3, y3)

Transformation of Coordinates Involving Pure Rotation

Transformation of Coordinates Involving Translation and Rotation

Polar Coordinates (r, θ)

Equation of Circle of Radius R, Center at (x, y)

Equation of Circle of Radius R Passing Through Origin

Ellipse with Center C(x0, y0) and Major Axis Parallel to x Axis

Parabola with Axis Parallel to x Axis

Hyperbola with Center C(x0, y0) and Major Axis Parallel to x Axis

#### Special Planes

Cycloid

Hypocycloid with Four Cusps

Cardioid

Catenary

Three-Leaved Rose

Four-Leaved Rose

Epicycloid

General Hypocycloid

Trochoid

Tractrix

Witch of Agnesi

Folium of Descartes

Involute of a Circle

Evolute of an Ellipse

Ovals of Cassini

Limacon of Pascal

Cissoid of Diocles

Spiral of Archimedes

#### Solid Analytic Geometric

Distance d Between Two Points P1(x1, y1, z1) and P2(x2, y2, z2)

Direction Cosines of Line Joining Points P1(x1, y1, z1) and P2(x2, y2, z2)

Relationship Between Direction Cosines

Equations of Line Joining P1 (x1, y1, z1) and P2(x2, y2, z2) in Standard Form

Equations of Line Joining P1(x1, y1, z1) and P2(x2, y2, z2) in Parametric Form

Angle e Between Two Lines with Direction Cosines l1, m1, n1 and l2, m2, n2

General Equation of a Plane

Equation of Plane Passing Through Points (x1, y1, z1), (x2, y2, z2), (x3, y3, z3)

Equation of Plane in Intercept Form

Equations of Line Through (x0, y0, z0) and Perpendicular to Plane

Cylindrical Coordinates (r, θ, z);Spherical Coordinates (r, θ, φ )

Equation of Sphere in Rectangular Coordinates

Equation of Sphere in Cylindrical Coordinates

Equation of Sphere in Spherical Coordinates

Equation of Ellipsoid with Center (x0, y0, z0) and Semi-axes a, b, c

Elliptic Cylinder with Axis as z Axis

Hyperboloid of One Sheet

Hyperboloid of Two Sheets

Elliptic Paraboloid

Hyperbolic Paraboloid

#### The Moments of Inertia of Rigid Bodies of Mass M

Thin rectangular plate with sides a, b

Circular cylinder of radius a and height h

Hollow circular cylinder of outer radius a, inner radius b and height h

Circular plate of radius a;Thin circular ring of radius a

Sphere of radius a

Hollow sphere of outer radius a and inner radius b

Hollow spherical shell of radius a

Ellipsoid with semi-axes a, b, c

Circular cone of radius a and height h

Torus with outer radius a and inner radius b

#### Trigonometric Functions

Trigonometric Functions for a Right Triangle

Relationship Between Degrees and Radians

Relationship Between Degrees and Radians

Relationships Among Trigonometric Functions

Signs and Variations of Trigonometric Functions

Exact Values for Trigonometric Functions of Various Angles

Functions of Negative Angles;Addition Formulas

Functions of Angles in All Quadrants

Relationships Among Functions of Angles in Quadrant I

Double Angle Formulas

Half Angle Formulas

Multiple Angle Formulas

Powers of Trigonometric Functions

Sum, Difference, and Product of Trigonometric Functions

Inverse Trigonometric Functions

Principal Values for Inverse Trigonometric Functions

Relations Between Inverse Trigonometric Functions

Law of Sines;Law of Cosines

Law of Tangents

Relationships Between Sides and Angles of a Spherical Triangle

Napier’s Rules for Right Angled Spherical Triangles

#### Exponential and Logarithmic Functions

Laws of Exponents

Laws of Logarithms

Change of Base of Logarithms

#### Hyperbolic Functions

Euler’s identities

Periodicity of Exponential Functions

Polar Form of Complex Numbers Expressed as an Exponential

De Moivre’s theorem

Logarithm of a Complex Number

Hyperbolic sine of x

Hyperbolic cosine of x

Hyperbolic tangent of x

Hyperbolic cotangent of x

Hyperbolic secant of x

Hyperbolic co-secant of x