False
False
False
The point whose Cartesian coordinates are (2, 0) has the polar coordinates R = 2, Θ = 0 .
The point whose Cartesian coordinates are (-3, -3) has the polar coordinates R = 3 sqrt(2), Θ = -0.75pi.
If the polar coordinates of a point P are (r,a) then the rectangular coordinates of P are x = rcos(a) and y = rsin(a).
False apex
the radius vector; and the vectorial angle the radius vector; and the vectorial angle
Some of them but not all. For example, uniqueness. The rectangular coordinates (x, y) represent a different point if either x or y is changed. This is also true for polar coordinate (r, a) but only if r > 0. For r = 0 the coordinates represent the same point, whatever a is. Thus (x, y) has a 1-to-1 mapping onto the plane but the polar coordinates don't.
True
absolute relative and polar coordinates definition
Coordinates. These may be Cartesian - ie distance from the origin in mutually perpendicular (orthogonal) directions. Or they may be polar. Polar coordinates consists of the length of the line joining the point to the origin together with the angles that the line makes with the various principal planes (or hyperplanes).
There are two main types: Cartesian coordinates and Polar coordinates.In n-dimensional Cartesian coordinates there are n axes which are [usually] orthogonal and which meet at a single point called the origin. The coordinates of any point in the n-space are defined by the ordered n-tuple whose terms refer to the distances of the point, from the origin, along each of the axes.In n-dimensional Polar coordinates, the point is located using its distance from the origin and the angles that this radial line makes with specified lines and planes.