Question

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

Answer 1

@Hero

Answer 2

@peachpi

Answer 3

@Luigi0210

Answer 4

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

Answer 5

can you calculate a value for r?

Answer 6

\[r = 5\sqrt{2}\]

Answer 7

yes. What about Θ?

Answer 8

\[\Theta = \frac{ 3\pi }{ 4 }, \frac{ 7\pi }{ 4 }\]

Answer 9

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°).

Answer 10

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°)