Help with a certain polar equation rule

Question

So I know x=rcos(theta) and y=rsin(theta). I was wondering if x^2=r^2cos^2(theta) is true? or is this incorrect and not be used to help me convert a polar equation to rectangular form.

Answer 1

That is absolutely correct.

It is also useful when converting from polar to rectangular or vice versa to remember the identity x² + y² = r² (since sin²Θ + cos²Θ = 1).