find a polar representation for the curve: x^2 + y^2 = 9

- anonymous

find a polar representation for the curve: x^2 + y^2 = 9

- katieb

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- myininaya

do you remember that
\[r^2=x^2+y^2\]

- anonymous

yeah so r = 3

- myininaya

satellite I having a moment here
doesn't r=3 include the equation r=-3?

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## More answers

- myininaya

you know when we are talking about polar equations?

- myininaya

i would include r=-3 just in case
because i'm having a memory issue right now

- anonymous

i think it is just
\[r=9\]

- myininaya

\[r^2=9 => r=\pm 3\]

- anonymous

r is the radius, always non negative. you want
\[r=f(\theta) but here r is constant

- anonymous

\[r=f(\theta)\]

- myininaya

you only need r=3

- anonymous

right i lunched it is
\[r=3\]

- anonymous

\[x=rcos \theta\]
\[y=rsin \theta\]
r=3\[r ^{2}\cos ^{2}\theta+r ^{2}\sin ^{2}\theta=9\]

- anonymous

yeah i got that far

- anonymous

yeah but this says
\[r=3\]

- anonymous

how do i simplify that?

- anonymous

too much work. r is the radius. it is a constant since you have a circle of radius 3

- myininaya

factor out r^2

- anonymous

did that

- myininaya

cos^2(theta)+sin^2(theta)=1

- anonymous

\[\cos ^{2}\theta+\sin ^{2}\theta=1\]

- anonymous

okay

- myininaya

you don't have to do it that way
the easiest is just recalling
\[r^2=x^2+y^2\]

- anonymous

you shouldn't think that hard! it is true that \[\cos ^{2}\theta+\sin ^{2}\theta=1\] but that is way too much work

- anonymous

so it's just r = 3 as my answeR?

- myininaya

yes

- anonymous

yes a circle looks like
\[r= number\]

- myininaya

r=3 will include all points from the center that have distance 3 from it

- anonymous

in polar coordinates a circle is just r = a number?

- anonymous

yes that is correct

- anonymous

r after all stands for "radius" and circle is a figure where the radius is constant

- anonymous

okay thank you!

- anonymous

http://www.wolframalpha.com/input/?i=r+%3D+3+

- anonymous

here is one where r is not constant
http://www.wolframalpha.com/input/?i=r+%3D+1%2Bsin%28theta%29

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