Question

express r=2cos(theta)+2sin(theta) as a cartesian function. this should have been fairly straight forward but i'm having problems with it

Answer 1

substitute x= rcos(theta), y= rsin(theta), sqrt(x^2 + y^2)=r
so x/r= cos(theta), y/r= sin(theta)

r= 2x/r + 2y/r
r^2= 2x + 2y
x^2+y^2= 2(x+y)

x^2 -2x-2y+y^2 =0
x^2 -2x +1 -1 +y^2 -2y +1 -1 =0
(x-1)^2 -1 +(y-1)^2 -1 =0
(x-1)^2 + (y-1)^2 = 2
this is a circle centered at (1,1) with radius sqrt(2)