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
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
Geodesy
GeoPosition ▪ Latitude ▪ Longitude ▪ LatitudeLongitude
GeoDirection ▪ GeoDestination ▪ GeoDisplacement
Astronomy
AstroPosition ▪ AstroAngularSeparation
Spherical Coordinates
ToSphericalCoordinates ▪ FromSphericalCoordinates ▪ CoordinateTransform
3D Rotations
EulerMatrix ▪ RollPitchYawMatrix ▪ AnglePath3D
Polar Plotting
PolarPlot ▪ ListPolarPlot ▪ SphericalPlot3D
Visual Rotation
Rotate ▪ RotationTransform ▪ ImageRotate