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

Question

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

anonymous · Answer

@Hero

anonymous · Answer

@peachpi

anonymous · Answer

@Luigi0210

anonymous · Answer

Polar coordinates are (r, Θ), where
$$r=\sqrt{x^2+y^2}$$ and $$\theta=\tan^{-1} \frac{ y }{ x }$$

anonymous · Answer

can you calculate a value for r?

anonymous · Answer

$$r = 5\sqrt{2}$$

anonymous · Answer

yes. What about Θ?

anonymous · Answer

$$\Theta = \frac{ 3\pi }{ 4 }, \frac{ 7\pi }{ 4 }$$

anonymous · Answer

sort of. First off the angles are in degrees.
(5, -5) is in the 4th quadrant, and 7π/4 or 315° is the angle in the 4th quadrant. So one pair is (5√2, 315°).

anonymous · Answer

To find the second pair, you can use the 2nd quadrant angle (basically a 180° rotation), but then you have to reflect the r over the origin. So the 2nd pair is (-5√2, 135°)