Question

let r = cos(theta) + sin(theta)
a. show that the equation in polar coordinates is a circle by writing the corresponding rectangular form.
b. provide the center and radius

anyone have any idea how to do this problem?

Answer 1

r = cos(theta) + sin(theta)
multipy both sides by r
and use r^2=x^2+y^2 and rcos(theta)=x and rsin(theta)=y
thus we have
r ^2= rcos(theta) + rsin(theta)
or x^2+y^2=x+y
or x^2+y^2-x-y=0
or x^2-2(1/2)x +1/4+y^2-2(1/2)y +1/4 =1/4+1/4
or (x-1/2)^2 +(y-1/2)^2= 1/2
circle with centre at(1/2,1/2) and radius=

Answer 2

r=1/sqrt(2)

Answer 3

thank you so much!