Search results
Results From The WOW.Com Content Network
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are
where a is the radius of the circle, (,) are the polar coordinates of a generic point on the circle, and (,) are the polar coordinates of the centre of the circle (i.e., r 0 is the distance from the origin to the centre of the circle, and φ is the anticlockwise angle from the positive x axis to the line connecting the origin to the centre of ...
A unit -sphere is the unit circle in the Euclidean plane, and its interior ... These two factors may be related using polar coordinates.
Vectors are defined in cylindrical coordinates by (ρ, φ, z), where ρ is the length of the vector projected onto the xy-plane, φ is the angle between the projection of the vector onto the xy-plane (i.e. ρ) and the positive x-axis (0 ≤ φ < 2π), z is the regular z-coordinate. (ρ, φ, z) is given in Cartesian coordinates by:
Since C = 2πr, the circumference of a unit circle is 2π. In mathematics, a unit circle is a circle of unit radius—that is, a radius of 1. [1] Frequently, especially in trigonometry, the unit circle is the circle of radius 1 centered at the origin (0, 0) in the Cartesian coordinate system in the Euclidean plane.
Just as the unit circle is important for planar polar coordinates, so the 3-sphere is important in the polar view of 4-space involved in quaternion multiplication. See polar decomposition of a quaternion for details of this development of the three-sphere.
A complex number can also be defined by its geometric polar coordinates: the radius is called the absolute value of the complex number, while the angle from the positive real axis is called the argument of the complex number. The complex numbers of absolute value one form the unit circle.
Another common coordinate system for the plane is the polar coordinate system. [7] A point is chosen as the pole and a ray from this point is taken as the polar axis. For a given angle θ, there is a single line through the pole whose angle with the polar axis is θ (measured counterclockwise from the axis to the line).