## anonymous one year ago Quick graphing question, thanks for helping! I posted the graph in the comments. I need to write the a coordinate in polar form, but make the radius a positive value. I also need to write point B in polar form as well. Thank You, this topic is really confusing. :P

1. anonymous
2. anonymous

@mathstudent55 @Nnesha @thomaster @sammixboo @pooja195 @freckles @inkyvoyd @k_lynn @mathmath333 @ybarrap @AkashdeepDeb @tanya123

3. anonymous

yup

4. ybarrap

Using Euler's Identity: $$\large Ae^{i\theta}=A(\cos \theta +i \sin \theta )$$ |dw:1434408079892:dw| Assuming each ring is 1 unit. Does this make sense?

5. anonymous

Isn't that B?

6. ybarrap

Yes, that's right

7. anonymous

ah cool.

8. anonymous

So for A it would be: -4(cos(5pi/6)+isin(5pi/6))

9. anonymous

?

10. ybarrap

Close. The radius is always positive. It's just the distance of the ring to the center. In this case it's 4, not -4. Also, write in polar form. What you have is almost correct, but keep in the exponential format. The right side of the equation is rectangular coordinates. Polar: $$e^{i\theta}$$ Rectangular $$\cos \theta +i \sin \theta$$ One is equal to the other.

11. anonymous

What exactly does it look like then?

12. ybarrap

|dw:1434408649310:dw| See the rectangle I drew above. That is point B in Polar form.

13. ybarrap
14. anonymous

I thought polar form was cos theta + isin theta. I thought rectangular was the coordinates (r, theta)?

15. ybarrap

The other way around. The first is called rectangular because cosine is the x value and sine is the y value |dw:1434409158978:dw|

16. ybarrap

Technically: $$(r\cos\theta,r\sin\theta)$$ is the rectangular coordinates $$(r,\theta)$$ Is Polar

17. ybarrap

$$r\exp^{i\theta}=r\left(\cos\theta+i\sin\theta \right)$$

18. anonymous

Should I write it as (r, theta)? I never formally learned e^i theta

19. ybarrap

Yes, that is also in Polar form

20. anonymous

Thanks! That was helpful!

21. ybarrap

$$\text{Rectangular: }(r\cos\theta,r\sin\theta)\\ \text{Polar: }(r,\theta)$$

22. anonymous

Gotcha, thanks for clearing that up! :)

23. anonymous

I gave you a medal

24. ybarrap

It was helpful that you knew the basics!

25. anonymous

Oh wait, one last question

26. anonymous

Should I write it as (4, 5pi/6), since r has to be positive? And if I were to graph (-3, pi/3) would it be on the -3 mark or the 3 mark?

27. ybarrap

If the second is in Polar form, it would be invalid because r > 0.

28. anonymous

That is odd, my worksheet says to graph it. Should I just write it in the -3 area?

29. ybarrap

The second one only makes sense if it is rectangular coordinates because r MUST always be positive. Imagine a circle. Can it ever have a negative radius?

30. anonymous

That is true. Do you think they mean that it should be graphed on the 3 mark?

31. ybarrap

(-3,pi/3) only makes sense if x=-3 and y=pi/3. Although, it is very unusual to specify a y-value using pi. But it is definitely NOT polar because of the -3.

32. ybarrap

Here's is the plot of that point - http://www.wolframalpha.com/input/?i=plot+%28-3%2Cpi%2F3%29

33. ybarrap

Here is that same point in Polar form - http://www.wolframalpha.com/input/?i=convert+%28-3%2Cpi%2F3%29+to+polar+form

34. anonymous

I think wolfram turned it into a complex number. I'll just graph it on 3 and see what my teacher says. Thanks for the help! I learned a lot!

35. anonymous

Part 1 should be (4, 5pi/6) right?

36. ybarrap

Yes it's right for point A That's what rectangular actually means, but you won't realize that until later. (x,y) is the same as ($$r\cos\theta,r\sin\theta$$) is the same as $$r(\cos\theta+i\sin \theta)$$ plus that exponential format, which you haven't studied yet.

37. anonymous

Alright, thanks!

38. ybarrap

You're welcome

39. anonymous

:)