Explanation Given: It is asked to show that the graph of the polar equation r = 2 a cos θ , a > 0 , , is a circle of radius a with center at ( a , 0 ) in rectangular coordinates. It is a known fact that each point in the polar coordinate system is given by ( r , θ ) where r is the distance from the pole (origin) to the point, and θ is the counter clockwise angle that is made with the point pole, and the positive x -axis. To convert back and forth between polar and rectangular coordinates, we have the following formulas: cos θ = x r x = r cos θ sin θ = y r y = r sin θ r 2 = ( r cos θ ) 2 + ( r sin θ ) 2 = x 2 + y 2 sin θ cos θ = y r x r tan θ = y x And ( x , y ) = ( r cos θ , r sin θ ) ...

11th Edition

ISBN: 9780135189405

Author: Michael Sullivan

Publisher: PEARSON

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Question

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

Chapter 9.2, Problem 87AYU

To determine

To show: The graph of the polar equation $r = 2 a cos θ, a > 0,$ is a circle of radius $a$ with center at $(a, 0)$ in rectangular coordinates.

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Chapter 9.2, Problem 86AYU

Chapter 9.2, Problem 88AYU

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Knowledge Booster

The graph of the polar equation r = 2 a cos θ , a > 0 , is a circle of radius a with center at ( a , 0 ) in rectangular coordinates.

Solution Summary: The author explains that the graph of the polar equation r = 2 a cos (a > 0) is an circle of radius with center at in rectangular coordinates.

To show: The graph of the polar equation $r = 2 a cos θ, a > 0,$ is a circle of radius $a$ with center at $(a, 0)$ in rectangular coordinates.

Want to see the full answer?

Chapter 9 Solutions

Additional Math Textbook Solutions

The graph of the polar equation r = 2 a cos θ , a &gt; 0 , is a circle of radius a with center at ( a , 0 ) in rectangular coordinates.

Solution Summary: The author explains that the graph of the polar equation r = 2 a cos (a > 0) is an circle of radius with center at in rectangular coordinates.

To show: The graph of the polar equation r = 2a cosθ, a>0, is a circle of radius a with center at (a, 0) in rectangular coordinates.

Want to see the full answer?

Chapter 9 Solutions

Additional Math Textbook Solutions

The graph of the polar equation r = 2 a cos θ , a > 0 , is a circle of radius a with center at ( a , 0 ) in rectangular coordinates.

To show: The graph of the polar equation $r = 2 a cos θ, a > 0,$ is a circle of radius $a$ with center at $(a, 0)$ in rectangular coordinates.