Question

Consider the polar curve defined by the function r(theta=theta cos(theta where 0 is less than or equal to theta and theta is less than or equal to 3pi/2

Answer 1

The polar curve will be:

r(θ) = cos(θ)

where 0 ≤ θ ≤ 3*π/2

This means that the radius of the polar curve depends on the angle in that way, for example, when θ = 0, r = 1

when θ = π/2, r = 0

and so on, so this curve will draw something like an infinity symbol, where the last segment is missing.

Answer 2

Given:

The function:

r(θ) = cos θ

where θ ≤ 3π/2

In the polar coordinates, we need to convert 3π/2 to degrees:

3π/2 = 3*180/2 = 270 degrees

This means that the function should be less than of equal to 270 degrees.