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

1. Astrophysics

$x = rcos \theta$ $y = rsin \theta$ For polar to cartesian coordinates. For cartesian to polar: $r^2 = x^2+y^2 ~~~~ \theta = \tan ^{-1} \left( \frac{ y }{ x } \right)$

2. Astrophysics

Note you want r so $r = \sqrt{x^2+y^2}$

3. anonymous

r = sqrt(8) or 2.828

4. Astrophysics

Sure, now find theta

5. anonymous

theta = 45

6. anonymous

now how do we find which quadrant it is in?

7. Astrophysics

Yeah but notice |dw:1435521133327:dw| theta gives us the value for the first and we need the fourth quadrant.

8. Astrophysics

Nice, you figured that out

9. anonymous

oh that makes sense

10. anonymous

so 315

11. Astrophysics

Yeah that seems reasonable so 7pi/4

12. anonymous

which is $\large(\frac{ \sqrt{2} }{ 2 }, \frac{ \sqrt{-2} }{ 2 })$

13. anonymous

on the unit circel

14. anonymous

circle*

15. Astrophysics

When you're looking for theta, you need unit circle :)

16. Astrophysics

Seems you got a good grasp on it though, nice work.

17. Astrophysics

$\sqrt{8} \implies 2\sqrt{2}$

18. anonymous

so what is the answer exactly? I need 2 points in Polar Coordinates of the original thing

19. anonymous

these are my options: (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°)

20. Astrophysics

Oh it wants two pairs

21. Astrophysics

So now what do you think the other will be?

22. anonymous

Im blanking @Astrophysics

23. anonymous

I think it's the third option. Am I right @zepdrix ?

24. Astrophysics

Oh I see a mistake

25. Astrophysics

What does $\theta = \tan^{-1}\left( \frac{ -2 }{ 2 } \right)$ give?

26. zepdrix

|dw:1435522015498:dw|So you found your first polar pair by rotating 315, and then extending outward 2sqrt2? Looks good.

27. anonymous

-45 @Astrophysics

28. zepdrix

|dw:1435522105721:dw|For your second option, you're rotating 180 degrees less around, and moving radially backwards.

29. zepdrix

ya third option looks good bro!

30. zepdrix

for the second coordinate pair i meant*

31. anonymous

Thanks both of you!

32. anonymous

I have another question but ill post a new form.

33. Astrophysics

If we could only give more than one medal :P

34. anonymous

haha true