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

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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

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

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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?
Isn't that B?
Yes, that's right
ah cool.
So for A it would be: -4(cos(5pi/6)+isin(5pi/6))
?
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.
What exactly does it look like then?
|dw:1434408649310:dw| See the rectangle I drew above. That is point B in Polar form.
See - https://en.wikipedia.org/wiki/Euler%27s_identity#Explanation
I thought polar form was cos theta + isin theta. I thought rectangular was the coordinates (r, theta)?
The other way around. The first is called rectangular because cosine is the x value and sine is the y value |dw:1434409158978:dw|
Technically: $$ (r\cos\theta,r\sin\theta) $$ is the rectangular coordinates $$ (r,\theta) $$ Is Polar
$$ r\exp^{i\theta}=r\left(\cos\theta+i\sin\theta \right) $$
Should I write it as (r, theta)? I never formally learned e^i theta
Yes, that is also in Polar form
Thanks! That was helpful!
$$ \text{Rectangular: }(r\cos\theta,r\sin\theta)\\ \text{Polar: }(r,\theta) $$
Gotcha, thanks for clearing that up! :)
I gave you a medal
It was helpful that you knew the basics!
Oh wait, one last question
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?
If the second is in Polar form, it would be invalid because r > 0.
That is odd, my worksheet says to graph it. Should I just write it in the -3 area?
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?
That is true. Do you think they mean that it should be graphed on the 3 mark?
(-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.
Here's is the plot of that point - http://www.wolframalpha.com/input/?i=plot+%28-3%2Cpi%2F3%29
Here is that same point in Polar form - http://www.wolframalpha.com/input/?i=convert+%28-3%2Cpi%2F3%29+to+polar+form
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!
Part 1 should be (4, 5pi/6) right?
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.
Alright, thanks!
You're welcome
:)

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