Use the formula r costheta to find the polar coordinates of

Use the formula r = costheta to find the polar coordinates of the points on the cardioid r = 2(1 + costheta) with the smallest x-coordinate. What is this smallest x-coordinate?

Solution

x = rcost

Hence x is minimum when t = pi

When t =pi, r = 2(1-1) =0

(0,pi) is the point

In rectangular coordinates x =0, y = 0