Why are polar coordinates for a point not unique?

Thus, the polar coordinates (r, θ) and (r, θ + 2Kπ) for any integer K represent the same complex number. Thus, the polar representation is not unique; by convention, a unique polar representation can be obtained by requiring that the angle given by a value of θ satisfying 0 ≤ θ < 2π or -π < θ ≤ π.

Do all points on the polar plane have unique polar coordinates?

As r ranges from 0 to infinity and θ ranges from 0 to 2π, the point P specified by the polar coordinates (r,θ) covers every point in the plane. However, even with that restriction, there still is some non-uniqueness of polar coordinates: when r=0, the point P is at the origin independent of the value of θ.

Do the polar coordinates represent the same point?

The two points corresponding to (−r,θ) and (r,θ) are reflection of each other with respect to the pole (origin) and therefore we may say that the polar (−r,θ) and (r,θ+π) represent the same point.

Are points in cylindrical coordinates unique?

Just as with polar coordinates, we usually limit 0≤θ<2π and r≥0 to descrease the non-uniqueness of cylindrical coordinates. However, when r=0, there is a non-uniqueness since the point P is on the z axis when r=0, independent of the value of θ.

Are polar points unique?

The rectangular coordinates of a point are unique, but the polar coordinates are not unique. Every point has infinitely many polar coordinate representations. and there are infinitely many other ways to represent this point.

What are plane polar coordinates?

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The radial coordinate is often denoted by r or ρ , and the angular coordinate by ϕ , θ , or t .

Are polar coordinates cylindrical?

Cylindrical coordinates are a simple extension of the two-dimensional polar coordinates to three dimensions. The polar coordinate r is the distance of the point from the origin. The polar coordinate θ is the angle between the x-axis and the line segment from the origin to the point.