Solution: Use vectors to prove that the diagonals of a rhombus are perpendicular
Chapter 10, Problem 79(choose chapter or problem)
Approximating Area 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.
(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.
Text Transcription:
r=8 cos theta
theta=0
theta
1/4,1/2
3/4
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