## Babynini one year ago Find two polar coordinate representations for the rectangular coordinate point (-6, 2 (sqroot3)), one with r>0, one with r<0 and both with <thetha<2pi

1. Babynini

For r I already got 4 (sqroot3) and -4 (Sqroot3)

2. Babynini

and then tan(theta)= -(2(sqroot3))/6

3. Babynini

@rvc :) I know you just got on. But if you're free!

4. rvc

ah bit busy dear :( @JoannaBlackwelder

5. Babynini

$\tan(\theta) = -\frac{ 2\sqrt{3} }{ 6 }$

6. JoannaBlackwelder

The tan equation looks good to me :-) Can you solve for theta?

7. Babynini

em theta = arctan (x) but i'm not sure how to keep it not in decimal form

8. Babynini

....?

9. JoannaBlackwelder

We will need to use the unit circle and the idea that tan is sin/cos

10. JoannaBlackwelder

http://www.mathsisfun.com/geometry/unit-circle.html Look down at the very bottom chart.

11. Babynini

I'm not finding anywhere that tangent equals that on the unit circle. It is sq3/3 at pi/6

12. Babynini

and -sq3/3 at 11pi/6

13. JoannaBlackwelder

Right, and -2sqrt3/6 is -sqrt3/3

14. Babynini

oh.. We can take the 6 and divide it by the 2 in the numerator?

15. JoannaBlackwelder

Yep, those can simplify, since they have a common factor of 2

16. JoannaBlackwelder

Do you see another one other than 11pi/6?

17. Babynini

5pi/6

18. Babynini

so how do I know which to choose? 11pi/6 or 5pi/6 ?

19. JoannaBlackwelder

Awesome! We are looking for 2 options, so both.

20. JoannaBlackwelder

And I don't get what you got for r. How did you get that?

21. Babynini

Give me a moment to type that up :)

22. JoannaBlackwelder

Oh, sorry, my mistake. You're rs are correct! :-)

23. JoannaBlackwelder

As long as you can combine them correctly.

24. JoannaBlackwelder

Into two pairs.

25. Babynini

$r^2=x^2+y^2$ $r^2=-6^2+(2\sqrt{3})^2$ $r^2=36+12 = \sqrt{48}$ Simplify and get $r=4\sqrt{3}$

26. Babynini

Right, how do I know how to pair them?

27. Babynini

(4 sq3, 5pi/6) (-4 sq3, 11pi/6) right? but i'm not sure how I got there xD or why

28. JoannaBlackwelder

Let's look at each of those graphically to see if they look like they are in the right spots.

29. JoannaBlackwelder

|dw:1434646002351:dw|

30. JoannaBlackwelder

Here is a rough graph of the rectangular coordinate.

31. Babynini

|dw:1434646256752:dw|

32. Babynini

Yeah?

33. JoannaBlackwelder

Yep, great!

34. Babynini

Fantastic, thanks :)

35. JoannaBlackwelder

No worries :-)