Question

Determine two pairs of polar coordinates for the point (2, -2) with 0° ≤ θ < 360°.

Answer 1

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

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

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

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

Answer 2

@iPwnBunnies

Answer 3

Ok, we're given a rectangular coordinate this time: (2,-2), in form (X,Y)
To convert to polar, use Pythagorean Theorem for r:
\[r = \sqrt{X^2 + Y^2}\]

Answer 4

k so r=√4+-4

Answer 5

Almost. Y is -2, but when you square -2, it becomes positive 4.

Answer 6

thats what i meant aha oops. So r=√8

Answer 7

Yes, which simplies to 2*sqrt(2)

Answer 8

Ok, for the angle. We use inverse tangent, or arctangent.
\[\tan^{-1}(\frac{Y}{X}) = \theta\]

Answer 9

alright

Answer 10

what do I do now?

Answer 11

This is another special angle.
arctan(-2/2) = arctan(-1) = 7pi/4, since the point (2,-2) is in Quadrant 4.

Answer 12

oh ok ya that makes sense

Answer 13

Good, we have our regular point then.
(2,-2) becomes (2*sqrt(2) , 7pi/4)

Answer 14

but how do we get that into the degree?

Answer 15

Oh, we have to convert it to degrees. But only one of those choices has that as an answer too.

Answer 16

When you convert the angle to degrees, you'll see.
Btw, when converting radians to degree, multiply by 180/pi

Answer 17

315 degrees, so the answer is (2√2,315 degrees), (-2√2,135 degrees)?

Answer 18

Yes. Remember when we were talking about the negative r values?
135 degrees is 180 degrees less than 315. So, 135 is exactly opposite of 315.
Since r is negative 2*sqrt(2), the point will be traced in the direction opposite of 135, which is 315.