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Graph the curve given by the equation r=2-3 cos(0). Label the exact polar coordinates of at least three points on the curve. 8-3n/4 8-5n/6 8-21/3 8=7n/6 0-5n/4 8-4n/3 8-n/2 8-3n/2 8-n/3 8-n/4 -8-n/6 60 8=5n/3 0=11m/6 e-7n/4

Graph the curve given by the equation r=2-3 cos(0). Label the exact polar coordinates of at least three points on the curve. 8-3n/4 8-5n/6 8-21/3 8=7n/6 0-5n/4 8-4n/3 8-n/2 8-3n/2 8-n/3 8-n/4 -8-n/6 60 8=5n/3 0=11m/6 e-7n/4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Graphing Polar Curves: A Study Guide** **Problem Statement:** 6. Graph the curve given by the equation \( r = 2 - 3\cos(\theta) \). Label the exact polar coordinates of at least three points on the curve. **Description of the Diagram:** The diagram provided is a polar coordinate system, often used to plot polar equations. It features concentric circles around a central point, representing different radii, and lines radiating out at regular angular intervals, labeled with angles in radians. **Angle Labels (counter-clockwise from positive x-axis):** - \( \theta = 0 \) - \( \theta = \pi/6 \) - \( \theta = \pi/4 \) - \( \theta = \pi/3 \) - \( \theta = \pi/2 \) - \( \theta = 2\pi/3 \) - \( \theta = 3\pi/4 \) - \( \theta = 5\pi/6 \) - \( \theta = \pi \) - \( \theta = 7\pi/6 \) - \( \theta = 5\pi/4 \) - \( \theta = 4\pi/3 \) - \( \theta = 3\pi/2 \) - \( \theta = 5\pi/3 \) - \( \theta = 7\pi/4 \) - \( \theta = 11\pi/6 \) **Graphing Instructions:** 1. **Understand the Equation:** - The equation \( r = 2 - 3\cos(\theta) \) is a limaçon with an inner loop due to the coefficient of \(\cos(\theta)\) being greater than the constant term. 2. **Convert Key Points:** - Calculate the polar coordinates \( (r, \theta) \) for key angles: - At \( \theta = 0 \): \( r = 2 - 3\cos(0) = 2 - 3 \times 1 = -1 \) - At \( \theta = \pi/2 \): \( r = 2 - 3\cos(\pi/2) = 2 - 3 \times 0 = 2 \) - At \( \theta = \pi \): \( r = 2 -
Transcribed Image Text:**Graphing Polar Curves: A Study Guide** **Problem Statement:** 6. Graph the curve given by the equation \( r = 2 - 3\cos(\theta) \). Label the exact polar coordinates of at least three points on the curve. **Description of the Diagram:** The diagram provided is a polar coordinate system, often used to plot polar equations. It features concentric circles around a central point, representing different radii, and lines radiating out at regular angular intervals, labeled with angles in radians. **Angle Labels (counter-clockwise from positive x-axis):** - \( \theta = 0 \) - \( \theta = \pi/6 \) - \( \theta = \pi/4 \) - \( \theta = \pi/3 \) - \( \theta = \pi/2 \) - \( \theta = 2\pi/3 \) - \( \theta = 3\pi/4 \) - \( \theta = 5\pi/6 \) - \( \theta = \pi \) - \( \theta = 7\pi/6 \) - \( \theta = 5\pi/4 \) - \( \theta = 4\pi/3 \) - \( \theta = 3\pi/2 \) - \( \theta = 5\pi/3 \) - \( \theta = 7\pi/4 \) - \( \theta = 11\pi/6 \) **Graphing Instructions:** 1. **Understand the Equation:** - The equation \( r = 2 - 3\cos(\theta) \) is a limaçon with an inner loop due to the coefficient of \(\cos(\theta)\) being greater than the constant term. 2. **Convert Key Points:** - Calculate the polar coordinates \( (r, \theta) \) for key angles: - At \( \theta = 0 \): \( r = 2 - 3\cos(0) = 2 - 3 \times 1 = -1 \) - At \( \theta = \pi/2 \): \( r = 2 - 3\cos(\pi/2) = 2 - 3 \times 0 = 2 \) - At \( \theta = \pi \): \( r = 2 -
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