anonymous 5 years ago find the cartesian equation of r = 8 sin thet + 8 cos theta

1. amistre64

its a circle centered at the irigin of radius 8 maybe?

2. anonymous

$r =\sqrt{x ^{2}+y ^{2}}$

3. amistre64

polars and parametrics aint my strong point ;)

4. anonymous

youre good at vectors :)

5. amistre64

yep, I can point at things all day lol

6. anonymous

haha, and good at planes

7. anonymous

maybe youre good at visualizing things?

8. amistre64

im pretty good at visualizing stuff

9. anonymous

ok we can use x = r cos theta, and y = r sin theta,

10. anonymous

so multiply both sides by r

11. amistre64

spinning polars tho.....not so much; aint had the practice

12. anonymous

$\sin \theta =x/r$

13. anonymous

ive read the vector stuff, it just wont stick. for some reason

14. amistre64

polars are just vector equations at heart :)

15. anonymous

i dont see that

16. amistre64

r = magnitude; <cos,sin> are the components

17. amistre64

r<cos(t),sin(t)> is the basi set up

18. anonymous

those are the cartesian components you mean

19. amistre64

in the plane, yes

20. amistre64

but polars define length(r) whih is the magnitude of a vector; and the <cos,sin> angles are the x and y components of a vector

21. amistre64

a vector function simply defines a curve or surface generated by the parametric equations for the vector components from teh origin

22. amistre64

and that is all a polar equation is

23. anonymous

come again, parametric equation for the vector components (the cartesian components?)

24. amistre64

(r,t) is a polar equation right? (radius,theta) this tells you how far to turn and how far to move

25. amistre64

thats all a vector is; an arrow indicating direction and length

26. anonymous

ok , lets use th for theta

27. anonymous

ok , so say again your statement

28. amistre64

which one lol

29. amistre64

r<cos(th),sin(th)> is the vector equivalent of a polar equation (r,th)

30. amistre64

or simpy <r cos(th), r sin(th)>

31. anonymous

vector , as in the cartesian components of the vector

32. amistre64

yes

33. amistre64

the point P(x,y) is the same as defining a vector from the origin as <x,y>

34. amistre64

the vector is an arrow pointing to the point

35. anonymous

right, that sometimes confuses me

36. anonymous

we write < x,y> for a vector, and P(x,y) for a point

37. amistre64

sometimes they write a vector as v(x,y) which confuses tha tmatter; i prefer the convention of just making it pointy to indicate its an arrow :)

38. anonymous

right, i like to distinguish between points (n tuples) and vectors

39. myininaya

cantorset i posted a proof for your viewing sorry it took me awhile to respond

40. anonymous

i cant find it, one sec

41. myininaya

k