Find the area of the region.
One petal of {eq}r=\cos (8\theta) {/eq}.
Question:
Find the area of the region.
One petal of {eq}r=\cos (8\theta) {/eq}.
Polar Coordinates; Area:
We'll analyze the graph and determine the range {eq}\theta\in[-\frac{\pi}{16},\frac{\pi}{16} ] {/eq} for one complete petal to appear. Then we'll use the formula for the area, {eq}A {/eq}, enclosed by the graph of a polar equation {eq}r=f(\theta) {/eq} with {eq}f(\theta)\ge 0 {/eq} in the range {eq}\theta \in [ {\theta_0},{\theta_1} ] {/eq}, namely:
{eq}A=\int_{\theta_0}^{\theta_1}\frac{1}{2}f^2(\theta)\,d\theta. {/eq}
Answer and Explanation: 1
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View this answerThe graph of the curve {eq}r=\cos (8\theta) {/eq} in polar coordinates
{eq}\begin{align*} x&=r\cos\theta,\\ y&=r\sin\theta, \end{align*} {/eq}
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Chapter 24 / Lesson 1Learn how to graph polar equations and plot polar coordinates. See examples of graphing polar equations. Transform polar to rectangular coordinates and vice versa.