the zenith side of the plane. This convention is used, in particular, for geographical coordinates, where the "zenith" direction is north and positive azimuth (longitude) angles are measured eastwards from some prime meridian. {| class="wikitable" style="text-align:center" |+ Major conventions |- ! coordinates !! corresponding local geographical directions !! right/left-handed |- | || || right |- | || || right |- | || || left |} Note: easting (), northing (), upwardness (). Local azimuth angle would be measured, e.g., counterclockwise from to in the case of . Unique coordinates Any spherical coordinate triplet specifies a single point of three-dimensional space. On the other hand, every point has infinitely many equivalent spherical coordinates. One can add or subtract any number of full turns to either angular measure without changing the angles themselves, and therefore without changing the point. It is also convenient, in many contexts, to allow negative radial distances, with the convention that is equivalent to for any , , and . Moreover, is equivalent to . If it is necessary to define a unique set of spherical coordinates for each point, one must restrict their ranges. A common choice is However, the azimuth is often restricted to the interval , or in radians, instead of . This is the standard convention for geographic longitude. For the polar angle , the range for inclination is equivalent to for elevation. In geography, the latitude is the elevation. Even with these restrictions, if is 0° or 180° (elevation is 90° or −90°) then the azimuth angle is arbitrary; and if is zero, both azimuth and inclination/elevation are arbitrary. To make the coordinates unique, one can use the convention that in these cases the arbitrary coordinates are zero. Plotting To plot a dot from its spherical coordinates , where is inclination, move units from the origin in the zenith direction, rotate by about the origin towards the azimuth reference direction, and rotate by about the zenith in the proper direction. Applications Just as the two-dimensional Cartesian coordinate system is useful on the plane, a two-dimensional spherical coordinate system is useful on the surface of a sphere. In this system, the sphere is taken as a unit sphere, so the radius is unity and can generally be ignored. This simplification can also be very useful when dealing with objects such as rotational matrices. Spherical coordinates are useful in analyzing systems that have some degree