anonymous 4 years ago find a polar representation for the curve: x^2 + y^2 = 9

1. myininaya

do you remember that $r^2=x^2+y^2$

2. anonymous

yeah so r = 3

3. myininaya

satellite I having a moment here doesn't r=3 include the equation r=-3?

4. myininaya

you know when we are talking about polar equations?

5. myininaya

i would include r=-3 just in case because i'm having a memory issue right now

6. anonymous

i think it is just $r=9$

7. myininaya

$r^2=9 => r=\pm 3$

8. anonymous

r is the radius, always non negative. you want $r=f(\theta) but here r is constant 9. anonymous \[r=f(\theta)$

10. myininaya

you only need r=3

11. anonymous

right i lunched it is $r=3$

12. anonymous

$x=rcos \theta$ $y=rsin \theta$ r=3$r ^{2}\cos ^{2}\theta+r ^{2}\sin ^{2}\theta=9$

13. anonymous

yeah i got that far

14. anonymous

yeah but this says $r=3$

15. anonymous

how do i simplify that?

16. anonymous

too much work. r is the radius. it is a constant since you have a circle of radius 3

17. myininaya

factor out r^2

18. anonymous

did that

19. myininaya

cos^2(theta)+sin^2(theta)=1

20. anonymous

$\cos ^{2}\theta+\sin ^{2}\theta=1$

21. anonymous

okay

22. myininaya

you don't have to do it that way the easiest is just recalling $r^2=x^2+y^2$

23. anonymous

you shouldn't think that hard! it is true that $\cos ^{2}\theta+\sin ^{2}\theta=1$ but that is way too much work

24. anonymous

so it's just r = 3 as my answeR?

25. myininaya

yes

26. anonymous

yes a circle looks like $r= number$

27. myininaya

r=3 will include all points from the center that have distance 3 from it

28. anonymous

in polar coordinates a circle is just r = a number?

29. anonymous

yes that is correct

30. anonymous

r after all stands for "radius" and circle is a figure where the radius is constant

31. anonymous

okay thank you!

32. anonymous
33. anonymous

here is one where r is not constant http://www.wolframalpha.com/input/?i=r+%3D+1%2Bsin%28theta%29