Question

Determine two pairs of polar coordinates for the point (4, -4) with 0° ≤ θ < 360°

Answer 1

Given coordinate points (x, y) = (4, -4) and it lies in IV quadrant.

tan θ = y/x = -4/4 = - 1.

We know that, tan θ is negative in II and IV quadrant.

In II quadrant, the angle θ = 3π/4.

In IV quadrant, the angle θ = 7π/4.

r2 = (x2 + y2) = (4)2 + (- 4)2 = 32

r = ± √(32) = ± 4√2.

Let us take positive value of r in IV quadrant (same quadrant) . So, polar coordinates points will be (4√2, 7π/4).

Let us take negative value of r in II quadrant. So, polar coordinates points will be (-4√2, 3π/4).

Polar coordinates points of (4,-4) within the angle range of 0 to 360 degree are (4√2, 7π/4) and (-4√2, 3π/4).