Question

Explain why a polar curve is not always bounded.

Answer 1

Answer: Polar curves do not need to be always bounded, suppose you are graphing something like a half-circle, the equation can be expressed as:

C(θ) = acos(θ) and 0 < θ < π

Another example may be if you want to describe a spiral, where the function may be thought as

C(r,θ) = r(θ)*cos(θ)

where r(θ) = A*θ, so when the angle increases, also the radius, and then the curve is not bounded.

Answer 2

There are lots of common polar curves that are bounded therefore a polar curve is not always bounded all the time. A polar curve is required to have an unbounded function (right side of r = f(Θ)) to be an unbounded polar. An example of an unbounded curve would be r = Θ for 0 ≤ Θ.