Solution
= Solution
At the stated point, the radial distance is $7\pi/2$, so $4\pi-t=7\pi/2$ and $t=\pi/2$. Differentiate the <parametric curve>:
$$
\dot x=-\sin t+(4\pi-t)\cos t,\qquad
\dot y=-\cos t-(4\pi-t)\sin t.
$$
At $t=\pi/2$, these are $\dot x=-1$ and $\dot y=-7\pi/2$. Since $\dot x\ne0$, the <tangent line> has finite <slope>
$$
\boxed{\frac{dy}{dx}=\frac{\dot y}{\dot x}=\frac{7\pi}{2}.}
$$