Question

Write the following polar equation in Cartesian coordinates:

r = sin (2θ) becomes
_______ = 0

(Write the equation so any square root has a positive coefficient.)

Answer 1

Remember that transformation between Cartesian and polar system are:
x=r*cos(α)
y=r*sin(α)
From this we can conclude that:
r=√(x^2 + y^2)

Using trigonometry transformations we can write:
r=sin(2α) = 2sin(α)cos(α)
Now we can multiply both sides with r^2:
r^3 = 2(r*sin(α))*(r*cos(α))

Now using some replacements we can write:
(x^2 + y^2)^(3/2) = 2*x*y