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Q 49.

Expert-verified

Calculus

Found in: Page 731

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.
$y = 0$

The required equation is $θ = 0$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given information.

The given equation in rectangular coordinates is:

$y = 0$

Step 2. Find the equation in rectangular coordinates.

$y = 0$

As we know that $y = r \sin θ$ in polar coordinates, then substitute the value of y,

$y = r \sin θ r \sin θ = 0 \sin θ = \frac{0}{r} \sin θ = 0 θ = 0 [\sin 0 = 0]$

Therefore, the equation in polar coordinates is $θ = 0$ .

Most popular questions for Math Textbooks

Measurements indicate that the orbital eccentricity of Mars is $0.0935$ and its semimajor axis is $1.517323951$ astronomical units.

(a) Write a Cartesian equation for the orbit of Mars.

(b) Do $x$ and $y$ have the same meaning as in Exercise 53?

(c) Give a polar coordinate equation for the orbit of Mars, assuming that the sun is the focus of the elliptical orbit.

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$r = \frac{3}{1 + \cos θ}$

Use polar coordinates to graph the conics in Exercises 44–51.

$r = \frac{2}{4 + \sin θ}$

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22–31.

$directrix x = 3, focus (0, 1)$

Use polar coordinates to graph the conics in Exercises 44–51.

$r = \frac{2}{4 + \cos θ}$

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