Question
Find the Cartesian form of the equation, r3 = 3r cosØ
Answers
Reiny
I will assume you meant
r^3 = 3r cosØ
Use: r^2 = x^2 + y^2 and x/r = cosØ
so if rcosØ = x
then 3rcosØ = 3x
and r^3 = r^2 r
= (x^2 + y^2)(x^2+y^2^(1/2)
= (x^2 + y^2)^(3/2)
r^3 + 3rcosØ ---> (x^2 + y^2)^(3/2) = 3x
r^3 = 3r cosØ
Use: r^2 = x^2 + y^2 and x/r = cosØ
so if rcosØ = x
then 3rcosØ = 3x
and r^3 = r^2 r
= (x^2 + y^2)(x^2+y^2^(1/2)
= (x^2 + y^2)^(3/2)
r^3 + 3rcosØ ---> (x^2 + y^2)^(3/2) = 3x