Question

How do I convert r=10cos(theta) to rectangular coordinates

Answer 1

what do you know about how rectangular and polar coordinates are related?

Answer 2

if you need to brush up on it then this might be of help: http://www.mathsisfun.com/polar-cartesian-coordinates.html

let me know if you are still stuck after this

Answer 3

I have an equation, but I don't have theta. I know that graphically r=10cos(theta) is a circle with a radius of 5, and the center of (5,0) but I have no idea how to find the rectangular coordinates. I know the equation of the circle is (x-5)^2+y^2=25 but I don't know if that is what the question is specifically asking for or not.

Answer 4

did you look at the link I gave above?

Answer 5

Yes I did and I am having troubles figuring out what to do. I know that (x-5)^2+y^2=25, and I know that r = x^2 +y^2, and I know that tan^-1(Y/X) = Theta, but I need some help putting this all together to convert the equation r=10cos(theta) to rectangular coordinates

Answer 6

you mean \(r^2=x^2+y^2\)

Answer 7

you are given:\[r=10\cos(\theta)\]multiply both sides by 'r' to get:\[r^2=10r\cos(\theta)\]can you see how to proceed from here?

Answer 8

It looks like we are trying to set up the equation to look like this: \[r ^{2} = x ^{2} + y ^{2}\] but I don't see what exactly can be done still because x and y is every single coordinate on the circle

Answer 9

no - that was in response to you stating "... I know that r = x^2 +y^2, ..."

Answer 10

the relation is not r = x^2 + y^2
its r^2 = x^2 + y^2

Answer 11

look at the equation I wrote above:\[r^2=10r\cos(\theta)\]notice that this can be written as:\[r^2=10(r\cos(\theta))\]now replace \(r^2\) and \(r\cos(\theta)\) with the rectangular equivalents

Answer 12

That was a typo. I meant \[r ^{2} = x ^{2} + y ^{2}\]

Answer 13

Which incidentally, that is also the equation of a circle...

Answer 14

polar and rectangular coordinates are related as follows:\[r^2=x^2+y^2\]\[x=r\cos(\theta)\]\[y=r\sin(\theta)\]\[\tan(\theta)=\frac{y}{x}\]
make use of this to convert this equation to rectangular coordinates:\[r^2=10r\cos(\theta)\]

Answer 15

So if I know the equation of the circle is \[(x-5)^{2} +y ^{2}=25\] and I know that \[r ^{2}=10(rcos(\theta))\] I can say that \[\tan ^{-1}(\theta) = \tan ^{-1}(0/-5) = 0 \] so then \[r^{2}=10(rcos(0))\]

Answer 16

Am I on the right track?

Answer 17

no

Answer 18

you are stating off from a polar equation:\[r=10\cos(\theta)\]we then multiply both sides by 'r' to get:\[r^2=10r\cos(\theta)\]we then make use of the relationships between polar and rectangular coordinates to get:\[x^2+y^2=10x\]this can then be re-arranged into the standard equation for a circle