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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
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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@mathstudent55 @Nnesha @thomaster @sammixboo @pooja195 @freckles @inkyvoyd @k_lynn @mathmath333 @ybarrap @AkashdeepDeb @tanya123

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Using 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
 one year ago
Best ResponseYou've already chosen the best response.0So for A it would be: 4(cos(5pi/6)+isin(5pi/6))

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Close. 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
 one year ago
Best ResponseYou've already chosen the best response.0What exactly does it look like then?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1dw:1434408649310:dw See the rectangle I drew above. That is point B in Polar form.

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1See  https://en.wikipedia.org/wiki/Euler%27s_identity#Explanation

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I thought polar form was cos theta + isin theta. I thought rectangular was the coordinates (r, theta)?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1The other way around. The first is called rectangular because cosine is the x value and sine is the y value dw:1434409158978:dw

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Technically: $$ (r\cos\theta,r\sin\theta) $$ is the rectangular coordinates $$ (r,\theta) $$ Is Polar

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1$$ r\exp^{i\theta}=r\left(\cos\theta+i\sin\theta \right) $$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Should I write it as (r, theta)? I never formally learned e^i theta

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that is also in Polar form

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Thanks! That was helpful!

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1$$ \text{Rectangular: }(r\cos\theta,r\sin\theta)\\ \text{Polar: }(r,\theta) $$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Gotcha, thanks for clearing that up! :)

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1It was helpful that you knew the basics!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wait, one last question

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Should 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
 one year ago
Best ResponseYou've already chosen the best response.1If the second is in Polar form, it would be invalid because r > 0.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0That is odd, my worksheet says to graph it. Should I just write it in the 3 area?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1The 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
 one year ago
Best ResponseYou've already chosen the best response.0That is true. Do you think they mean that it should be graphed on the 3 mark?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1(3,pi/3) only makes sense if x=3 and y=pi/3. Although, it is very unusual to specify a yvalue using pi. But it is definitely NOT polar because of the 3.

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Here's is the plot of that point  http://www.wolframalpha.com/input/?i=plot+%283%2Cpi%2F3%29

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Here is that same point in Polar form  http://www.wolframalpha.com/input/?i=convert+%283%2Cpi%2F3%29+to+polar+form

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0Part 1 should be (4, 5pi/6) right?

ybarrap
 one year ago
Best ResponseYou've already chosen the best response.1Yes 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.
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