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:
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Coordinating Conjunctions
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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 $z$ coordinate is the same in both systems, and the correspondence between cylindrical $(\rho,\varphi)$ and Cartesian $(x,y)$ are the same as for polar coordinates, namely $x = \rho \cos \varphi; \, y = \rho \sin \varphi$.
- The spherical coordinates (radius $r$, inclination $\theta$, azimuth $\varphi$) of a point can be obtained from its Cartesian coordinates ($x$, $y$, $z$) by the formulae:
- A cylindrical coordinate system with origin $O$, polar axis $A$, and longitudinal axis $L$.
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Polar Coordinates
- This is called the Cartesian coordinate system.
- Such definitions are called polar coordinates.
- Polar coordinates in $r$ and $\theta$ can be converted to Cartesian coordinates $x$ and $y$.
- A set of polar coordinates.
- The $x$ Cartesian coordinate is given by $r \cos \theta$ and the $y$ Cartesian coordinate is given by $r \sin \theta$.
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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.
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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 $(0,3)$ is the same as the polar coordinate $(3,\frac {\pi}{2})$ as plotted on the two grids above.
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Three-Dimensional Coordinate Systems
- The three-dimensional coordinate system expresses a point in space with three parameters, often length, width and depth ($x$, $y$, and $z$).
- Each parameter is perpendicular to the other two, and cannot lie in the same plane. shows a Cartesian coordinate system that uses the parameters $x$, $y$, and $z$.
- 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
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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.
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Introduction to the Polar Coordinate System
- The polar coordinate system is an alternate coordinate system where the two variables are $r$ and $\theta$, instead of $x$ and $y$.
- When we think about plotting points in the plane, we usually think of rectangular coordinates $(x,y)$ 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 $r$ or $ρ$ , and the angular coordinate by $ϕ$, $θ$, or $t$.
- In green, the point with radial coordinate $3$ and angular coordinate $60$ degrees or $(3,60^{\circ})$.
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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.
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Double Integrals in Polar Coordinates
- In $R^2$, 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 $P(x, y)$ in Cartesian coordinates switch to their respective points in polar coordinates.
- The polar coordinates $r$ and $\varphi$ can be converted to the Cartesian coordinates $x$ and $y$ by using the trigonometric functions sine and cosine:
- The Cartesian coordinates $x$ and $y$ can be converted to polar coordinates $r$ and $\varphi$ with $r \geq 0$ and $\varphi$ 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