Determine two pairs of polar coordinates for the point (3, -3) with 0° ≤ θ < 360°.

Answer 1

The rectangular coordinate point : (x, y) = (3, -3).

The point (3, -3) lies in fourth quadrant.

tan θ = y/x = -3/3 = - 1.

The value of tan θ is negative in second and fourth quadrant.

In second quadrant, the angle θ = 3π/4.

In fourth quadrant, the angle θ = 7π/4.

r² = (x² + y²) = (3)² + (- 3)² = 9 + 9 = 18.

r = ± √(18) = ± 3√2.

Because θ was chosen to be in the same quadrant (fourth) as (x, y), we should be use a positive value of r.

The polar coordinates points is (3√2, 7π/4).

Because θ was not chosen to be in the same quadrant (second) as (x, y), we should be use a negative value of r.

The polar coordinates points is (-3√2, 3π/4).

The polar coordinates points are (3√2, 7π/4) and (-3√2, 3π/4).