Answer: Use vectors to prove that a parallelogram is a rectangle if and only if its

Chapter 10, Problem 80

(choose chapter or problem)

Approximate Area   Consider the circle \(r=3 \sin \theta\).

(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.

(c) Use the table in part (b) to approximate the values of \(\theta\) for which the sector of the circle composes \(\frac{1}{8}, \frac{1}{4}\), and \(\frac{1}{2}\) 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 \(\frac{1}{8}, \frac{1}{4}\), and \(\frac{1}{2}\) of the total area of the circle.

Text Transcription:

r=3 sin theta

theta=0

theta

1/8, 1/4

1/2