Thread: Cartesian equation for a curve

Hey guys i need help with this question for an assignment.

Find a Cartesian equation for the curve and identify it:
r = 2sin(θ) + 2cos(θ)

i tried multipliying everything by r, getting:
r^2 = 2rsin(θ) + 2rcos(θ)
then making r^2 = x^2 + y^2 and making rsin(θ)=y and rcos(θ)=x.

but that didn't work :/.

please help

Originally Posted by CenturionMonkey

Hey guys i need help with this question for an assignment.

Find a Cartesian equation for the curve and identify it:
r = 2sin(θ) + 2cos(θ)

i tried multipliying everything by r, getting:
r^2 = 2rsin(θ) + 2rcos(θ)
then making r^2 = x^2 + y^2 and making rsin(θ)=y and rcos(θ)=x.

but that didn't work :/.

please help

sure it did, you just didn't finish ...

r^2 = 2rsin(θ) + 2rcos(θ)

x^2 + y^2 = 2y + 2x

x^2 - 2x + y^2 - 2y = 0

x^2 - 2x + 1 + y^2 - 2y + 1 = 2

(x - 1)^2 + (y - 1)^2 = 2

what's this an equation for?

thanks, yeah it worked out actually the way i did it. Its just that for some reason my assignemt wouldn't accept the answer unless i factored out a y. :S.

thanks anyway