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

1. Mertsj

Jim will take over.

2. jim_thompson5910

similar to what Mertsj drew |dw:1437356798358:dw|

3. jim_thompson5910

|dw:1437356851407:dw|

4. jim_thompson5910

|dw:1437356864345:dw|

5. jim_thompson5910

and that 45 is actually -45 degrees because we're going clockwise instead of counterclockwise

6. egbeach

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

7. jim_thompson5910

|dw:1437357081640:dw|

8. jim_thompson5910

one possible representation is (2*sqrt(2), 315)

9. jim_thompson5910

315 - 180 = 135 degrees |dw:1437357159428:dw| so another possible polar representation is (-2*sqrt(2), 135) the negative r value means you walk backwards 2*sqrt(2) units while facing the 135 degree direction

10. anonymous

You can determine by this way: (2, -2) that is x =2, y =-2 hence $$r=\sqrt{2^2+(-2)^2}=2\sqrt2$$ $$\theta =arctan(\dfrac{y}{x}) = arctan(-1)$$ Hence on the unit circle, $$\theta = 3\pi/4$$ or $$\theta =-\pi/4$$ |dw:1437357509404:dw|

11. anonymous

Therefore, the first pair is $$(2\sqrt2, -\pi/4)$$

12. anonymous

Moreover, the opposite side of the terminal point will stop at 3pi/4. But to get the point (2,-2) we need negative value of r, hence, the second point will be $$(-2\sqrt2, 3\pi/4)$$ |dw:1437357640591:dw|