Which equation correctly converts rectangular coordinates to polar coordinates?

The equation that accurately converts rectangular coordinates to polar coordinates is r = √(x² + y²). This relationship defines the radius in polar coordinates (r) as the distance from the origin to the point in rectangular coordinates (x, y). By applying the Pythagorean theorem, where r represents the hypotenuse of a right triangle and x and y are the legs, we derive that the squared distance r² is equal to the sum of the squares of x and y. Therefore, solving for r gives us the aforementioned equation.

Using this formula allows us to transform Cartesian coordinates (x, y) into their polar equivalent, ensuring that we can express the distance from the origin correctly. The other options either represent relationships that are not characteristic of polar conversion or mistakenly formulate the trigonometric components without appropriate context.