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).
the radius vector; and the vectorial angle the radius vector; and the vectorial angle
False apex
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.
In polar coordinates, the curl of a vector field represents how much the field is rotating around a point. The relationship between the curl and the representation in polar coordinates is that the curl can be calculated using the polar coordinate system to determine the rotational behavior of the vector field.
The curl of polar coordinates is a mathematical operation that measures the rotation or circulation of a vector field around a point in the polar coordinate system. It helps to understand the flow and behavior of the vector field in a two-dimensional space.
True
absolute relative and polar coordinates definition