Which is the parametric form of the polar equation r=-4 theta?

A. x=-4 cos theta, y=-4 sin theta

B. x=-4 theta cos theta, y=-4 theta sin theta

C. x=-theta cos theta, y=-theta cos theta

Answer: Option B.

Step-by-step explanation:

we have that r = 4*θ

(you writted a negative equation, but we can never have a negative radius)

We also have that:

r = √ (x^2 + y^2) = 4*θ

We can use the relationship cos (x) ^2 + sin (x) ^2 = 1

and write X = A*cos (θ) and Y = A*sin (θ)

and now we have:

r = √ ((A*cos (θ)) ^2 + (A*sin (θ)) ^2) = √ (A) ^2 = 4*θ

So the correct option is:

x = 4*θ*cos (θ) or - 4*θ*cos (θ)

y = 4*θ*sin (θ) or - 4*θ*cos (θ)

(We can have the positive or negative options because we are squaring the term, so the sign does not matter)

The correct option then is B