Angles and Polar Coordinates

Representing complex numbers, vectors, or positions using angles is a fundamental construction in calculus and geometry, and many applied areas like geodesy. The Wolfram Language offers a flexible variety of ways of working with angles: as numeric objects in radians, Quantity objects with any angular unit, or degree-minute-second (DMS) lists and strings. These forms are understood and automatically converted by the functions working with angles, in particular functions converting between polar or spherical coordinates and Cartesian coordinates, as well as the geodesy functionality.

Specifying Angles

Degree (°) constant to convert from radians to degrees

FromDMS convert from degrees-minutes-seconds format

DMSList  ▪  DMSString

Quantity explicitly specify units for angles

Computing Angles

VectorAngle angle between vectors

PlanarAngle planar angle defined by three points

SolidAngle solid angle subtended by a region

PolygonAngle vertex angle of a polygon

PolyhedronAngle vertex and edge angles of a polyhedron

DihedralAngle angle between planes in 3D

Vectors & Paths

AngleVector create a vector at a specified angle

CirclePoints equally distributed points around a circle (regular -gon)

AnglePath form a path from a sequence of "turtle-like" turns and motions

Coordinate Transformations

FromPolarCoordinates convert from {r,θ} to {x,y}

ToPolarCoordinates convert from {x,y} to {r,θ}

RotationMatrix rotation matrix in any number of dimensions

Complex Numbers

AbsArg convert a complex number to polar form

Abs  ▪  Arg  ▪  Sign  ▪  ReIm

Geodesy

GeoPosition  ▪  Latitude  ▪  Longitude  ▪  LatitudeLongitude

GeoDirection  ▪  GeoDestination  ▪  GeoDisplacement

Spherical Coordinates

ToSphericalCoordinates  ▪  FromSphericalCoordinates  ▪  CoordinateTransform

3D Rotations

EulerMatrix  ▪  RollPitchYawMatrix  ▪  AnglePath3D

Polar Plotting

PolarPlot  ▪  ListPolarPlot  ▪  SphericalPlot3D

Visual Rotation

Rotate  ▪  RotationTransform  ▪  ImageRotate

Geometric Constructions

AngleBisector  ▪  TriangleConstruct  ▪  ...