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Even with these restrictions, if the polar angle (inclination) is 0° or 180°—elevation is −90° or +90°—then the azimuth angle is arbitrary; and if r is zero, both azimuth and polar angles are arbitrary. To define the coordinates as unique, the user can assert the convention that (in these cases) the arbitrary coordinates are set to zero.
A polar grid with several angles, increasing in counterclockwise orientation and labelled in degrees. The radial coordinate is often denoted by r or ρ, and the angular coordinate by φ, θ, or t. The angular coordinate is specified as φ by ISO standard 31-11. However, in mathematical literature the angle is often denoted by θ instead.
It assigns three numbers (known as coordinates) to every point in Euclidean space: radial distance r, polar angle θ , and azimuthal angle φ . The symbol ρ ( rho ) is often used instead of r . In geometry , a coordinate system is a system that uses one or more numbers , or coordinates , to uniquely determine the position of the points or ...
The concept of the position angle is inherited from nautical navigation on the oceans, where the optimum compass course is the course from a known position s to a target position t with minimum effort. Setting aside the influence of winds and ocean currents, the optimum course is the course of smallest distance between the two positions on the ...
Standard names for the coordinates in the three axes are abscissa, ordinate and applicate. [9] The coordinates are often denoted by the letters x, y, and z. The axes may then be referred to as the x-axis, y-axis, and z-axis, respectively. Then the coordinate planes can be referred to as the xy-plane, yz-plane, and xz-plane.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
Conversely, it is easily shown that if a, b, c and d are constants and a, b, and c are not all zero, then the graph of the equation + + + =, is a plane having the vector = (,,) as a normal. [ citation needed ] This familiar equation for a plane is called the general form of the equation of the plane.
The ISO standard 31-11 recommends (ρ, φ, z), where ρ is the radial coordinate, φ the azimuth, and z the height. However, the radius is also often denoted r or s , the azimuth by θ or t , and the third coordinate by h or (if the cylindrical axis is considered horizontal) x , or any context-specific letter.