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

- anonymous

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- katieb

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- anonymous

http://assets.openstudy.com/updates/attachments/557f1888e4b05cad71f26eb0-notsephiroth-1434392738273-polargraph.png

- anonymous

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

- anonymous

yup

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## More answers

- 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?

- anonymous

Isn't that B?

- ybarrap

Yes, that's right

- anonymous

ah cool.

- anonymous

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

- anonymous

?

- 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.

- anonymous

What exactly does it look like then?

- ybarrap

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

- ybarrap

See - https://en.wikipedia.org/wiki/Euler%27s_identity#Explanation

- anonymous

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

- 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|

- ybarrap

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

- ybarrap

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

- anonymous

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

- ybarrap

Yes, that is also in Polar form

- anonymous

Thanks! That was helpful!

- ybarrap

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

- anonymous

Gotcha, thanks for clearing that up! :)

- anonymous

I gave you a medal

- ybarrap

It was helpful that you knew the basics!

- anonymous

Oh wait, one last question

- 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?

- ybarrap

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

- anonymous

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

- 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?

- anonymous

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

- 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.

- ybarrap

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

- ybarrap

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

- 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!

- anonymous

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

- 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.

- anonymous

Alright, thanks!

- ybarrap

You're welcome

- anonymous

:)

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