MATHCRAVE FORMULA
MathCrave Math

# AI Math Formula

## 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;

• 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;

• 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;

• 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;

• 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

• Hollow spherical shell of radius a

• Ellipsoid with semi-axes a, b, c

• Circular cone of radius a and height h

#### 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