Question

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

Answer 1

(3 square root 2, 315°), (-3 square root 2, 135°)

(3 square root 2, 135°), (-3 square root 2, 315°)

(3 square root 2, 45°), (-3 square root 2, 225°)

(3 square root 2, 225°), (-3 square root 2, 45°)
These are the options.

Answer 2

the point (3,3) has distance of 3sqrt2 from origin at angle 45
if you draw line in opposite direction...r= -3root2 you end up at point with angle 225
in general if you have a point , the pair of possible coordinates are:
\[(r,\theta)\leftarrow \rightarrow (-r,\theta + 180)\]

Answer 3

Thanks (: @dumbcow