**Problem : **
Given a point in rectangular coordinates (*x*, *y*), express it in polar
coordinates (*r*, *θ*) two different ways such that 0≤*θ* < 2*Π*:
(*x*, *y*) = (1,).

(*r*, *θ*) = (2,),(- 2,).

**Problem : **
Given a point in rectangular coordinates (*x*, *y*), express it in polar
coordinates (*r*, *θ*) two different ways such that 0≤*θ* < 2*Π*:
(*x*, *y*) = (- 4, 0).

(*r*, *θ*) = (4, *Π*),(- 4, 0).

**Problem : **
Given a point in polar coordinates (*r*, *θ*), express it in rectangular
coordinates (*x*, *y*): (*r*, *θ*) = (3,).

(*x*, *y*) = (,).

**Problem : **
Given a point in polar coordinates (*r*, *θ*), express it in rectangular
coordinates (*x*, *y*): (*r*, *θ*) = (1,).

(*x*, *y*) = (- ,).

**Problem : **
Given a point in polar coordinates (*r*, *θ*), express it in rectangular
coordinates (*x*, *y*): (*r*, *θ*) = (0,).

(*x*, *y*) = (0, 0).

**Problem : **
How many different ways can a point be expressed in polar coordinates such that
*r* > 0?

An infinite number.

(*r*, *θ*) = (*r*, *θ* +2*nΠ*), where

*n* is an
integer.

**Problem : **
How many different ways can a point be expressed in polar coordinates such that
0≤*θ* < 2*nΠ*?

2*n*. In every cycle of

2*Π*, there are two pairs of polar coordinates,

(*r*, *θ*) and

(- *r*, *θ* + (2*n* + 1)*Π*) for every point.