Approximating Area $\quad$ Consider the circle $r=8 \cos \theta$
(a) Find the area of the circle.
(b) Complete the table giving the areas $A$ of the sectors of the circle between $\theta=0$ and the values of $\theta$ in the table.$$
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline \boldsymbol{\theta} & 0.2 & 0.4 & 0.6 & 0.8 & 1.0 & 1.2 & 1.4 \\
\hline \boldsymbol{A} & & & & & & & \\
\hline
\end{array}
$$(c) Use the table in part (b) to approximate the values of $\theta$ for which the sector of the circle composes $\frac{1}{4}, \frac{1}{2}$, and $\frac{3}{4}$ of the total area of the circle.
(d) Use a graphing utility to approximate, to two decimal places, the angles $\theta$ for which the sector of the circle composes $\frac{1}{4}, \frac{1}{2}$, and $\frac{3}{4}$ of the total area of the circle.
(e) Do the results of part (d) depend on the radius of the circle? Explain.