coordinate

(noun)

a number representing the position of a point along a line, arc, or similar one-dimensional figure

Examples of coordinate in the following topics:

  • Coordinating Conjunctions

  • Cylindrical and Spherical Coordinates

    • Cylindrical and spherical coordinates are useful when describing objects or phenomena with specific symmetries.
    • While Cartesian coordinates have many applications, cylindrical and spherical coordinates are useful when describing objects or phenomena with specific symmetries.
    • Then the zzz coordinate is the same in both systems, and the correspondence between cylindrical (ρ,φ)(\rho,\varphi)(ρ,φ) and Cartesian (x,y)(x,y)(x,y) are the same as for polar coordinates, namely x=ρcosφ;y=ρsinφx = \rho \cos \varphi; \, y = \rho \sin \varphix=ρcosφ;y=ρsinφ.
    • The spherical coordinates (radius rrr, inclination θ\thetaθ, azimuth φ\varphiφ) of a point can be obtained from its Cartesian coordinates (xxx, yyy, zzz) by the formulae:
    • A cylindrical coordinate system with origin OOO, polar axis AAA, and longitudinal axis LLL.
  • Polar Coordinates

    • This is called the Cartesian coordinate system.
    • Such definitions are called polar coordinates.
    • Polar coordinates in rrr and θ\thetaθ can be converted to Cartesian coordinates xxx and yyy.
    • A set of polar coordinates.
    • The xxx Cartesian coordinate is given by rcosθr \cos \thetarcosθ and the yyy Cartesian coordinate is given by rsinθr \sin \thetarsinθ.
  • The Cartesian System

    • A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to the two axes.
    • Any point in the first quadrant has both positive x and y coordinates.
    • The third quadrant has both negative x and y coordinates.
    • The four quadrants of a Cartesian coordinate system.
    • The four quadrants of a Cartesian coordinate system.
  • Converting Between Polar and Cartesian Coordinates

    • When given a set of polar coordinates, we may need to convert them to rectangular coordinates.
    • To convert rectangular coordinates to polar coordinates, we will use two other familiar relationships.
    • A right triangle with rectangular (Cartesian) coordinates and equivalent polar coordinates.
    • A right triangle with rectangular (Cartesian) coordinates and equivalent polar coordinates.
    • The rectangular coordinate (0,3)(0,3)(0,3) is the same as the polar coordinate (3,π2)(3,\frac {\pi}{2})(3,​2​​π​​) as plotted on the two grids above.
  • Three-Dimensional Coordinate Systems

    • The three-dimensional coordinate system expresses a point in space with three parameters, often length, width and depth (xxx, yyy, and zzz).
    • Each parameter is perpendicular to the other two, and cannot lie in the same plane. shows a Cartesian coordinate system that uses the parameters xxx, yyy, and zzz.
    • This is a three dimensional space represented by a Cartesian coordinate system.
    • The cylindrical coordinate system is like a mix between the spherical and Cartesian system, incorporating linear and radial parameters.
    • Identify the number of parameters necessary to express a point in the three-dimensional coordinate system
  • Increasing Coordination

    • Increasing coordination helps organizations to maintain efficient operations through communication and control.
    • Coordination is the act of organizing and enabling different people to work together to achieve an organization's goals.
    • Coordination is simply the managerial ability to maintain operations and ensure they are properly integrated with one another; therefore, increasing coordination is closely related to improving managerial skills.
    • The management team must pay special attention to issues related to coordination and governance and be able to improve upon coordination through effective management.
    • In practice, coordination involves a delicate balance between centralization and decentralization.
  • Introduction to the Polar Coordinate System

    • The polar coordinate system is an alternate coordinate system where the two variables are rrr and θ\thetaθ, instead of xxx and yyy.
    • When we think about plotting points in the plane, we usually think of rectangular coordinates (x,y)(x,y)(x,y) in the Cartesian coordinate plane.
    • The distance from the pole is called the radial coordinate or radius, and the angle is called the angular coordinate, polar angle, or azimuth.
    • The radial coordinate is often denoted by rrr or $ρ$ , and the angular coordinate by $ϕ$, $θ$, or ttt.
    • In green, the point with radial coordinate 333 and angular coordinate 606060 degrees or (3,60∘)(3,60^{\circ})(3,60​∘​​).
  • Reactions of Coordination Compounds

    • Many metal-containing compounds consist of coordination complexes.
    • The central atom or ion, together with all ligands, comprise the coordination sphere.
    • The central atoms or ion and the donor atoms comprise the first coordination sphere.
    • Coordination refers to the coordinate covalent bonds (dipolar bonds) between the ligands and the central atom.
    • As applied to coordination chemistry, this meaning has evolved.
  • Double Integrals in Polar Coordinates

    • In R2R^2R​2​​, if the domain has a cylindrical symmetry and the function has several particular characteristics, you can apply the transformation to polar coordinates, which means that the generic points P(x,y)P(x, y)P(x,y) in Cartesian coordinates switch to their respective points in polar coordinates.
    • The polar coordinates rrr and φ\varphiφ can be converted to the Cartesian coordinates xxx and yyy by using the trigonometric functions sine and cosine:
    • The Cartesian coordinates xxx and yyy can be converted to polar coordinates rrr and φ\varphiφ with r≥0r \geq 0r≥0 and φ\varphiφ in the interval $(−\pi, \pi]$:
    • In general, the best practice is to use the coordinates that match the built-in symmetry of the function.
    • This figure illustrates graphically a transformation from cartesian to polar coordinates
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