Mathematics

Problem

The polar curve

r=3\cos 2\theta

is traced for

0\le\theta\le2\pi

. (a) Find the Cartesian coordinates of the point on the curve that corresponds to

\theta=\dfrac{\pi}{8}

. (b) Compute the slope

\dfrac{dy}{dx}

of the curve at

\theta=\dfrac{\pi}{8}

. (c) Express the equation of the tangent line at that point in the implicit linear form

Ax+By=C

, where

A

B

, and

C

are simplified exact values.