Question

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

Answer 1

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

Answer 2

yeah so r = 3

Answer 3

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

Answer 4

you know when we are talking about polar equations?

Answer 5

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

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

\[r=f(\theta)\]

Answer 10

you only need r=3

Answer 11

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

Answer 12

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

Answer 13

yeah i got that far

Answer 14

yeah but this says
\[r=3\]

Answer 15

how do i simplify that?

Answer 16

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

Answer 17

factor out r^2

Answer 18

did that

Answer 19

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

Answer 20

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

Answer 21

okay

Answer 22

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

Answer 23

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

Answer 24

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

Answer 25

yes

Answer 26

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

Answer 27

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

Answer 28

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

Answer 29

yes that is correct

Answer 30

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

Answer 31

okay thank you!

Answer 32

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

Answer 33

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