Determine two pairs of polar coordinates for the point (5, -5) with 0° ≤ θ < 360°.

Answer 1

Step 1:

The rectangular point is .

If is a point rectangular coordinates  then, polar coordinates  are defined as

  and .

Here .

Substitute in .

Substitute in .

is negative in second and fourth quadrants.

and .

and .

Two pairs of polar coordinates of the point are  and .

Step 2:

The polar coordinates: .

.

Polar coordinates .

Substitute the values of in .

.

Substitute the values of in .

.

.

Solution:

Two pairs of polar coordinates of the point and .

Rectangular coordinates: .