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Chapter 9: Q. 3 (page 746)

How can the graph of an equation $r = f (θ)$ in the $θ - r$ -plane be used to provide information about the graph of the same equation in the polar plane?

Short Answer

Expert verified

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Step by step solution

Step 1. Given information

The equation in the polar form is:

$r = f (θ)$

Step 2.

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Most popular questions from this chapter

In Exercises 48–55 convert the equations given in rectangular coordinates to equations in polar coordinates.

$y = x$

Let $A > B > 0$ . Show that the distance from any point on the graph of the curve with equation $\frac{x^{2}}{A^{2}} + \frac{y^{2}}{B^{2}} = 1$ to the point $(- C, 0) is D_{2} = \frac{A^{2} + C x}{A^{2}}, where C = \sqrt{A^{2} - B^{2}} .$

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression

The integral is $\frac{1}{2} \int_{0}^{2 π} {(1 + \sin θ)}^{2} d θ$

in exercise 31-36 find a definite integral that represents the length of the specified polar curve, and then use graphing calculator or computer algebra system to approximate the value of integral

The entire limacon $r = 1 + 2 \sin θ$

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38–43.

foci (0, \pm 4), directrices y = \pm 2

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How can the graph of an equation $r = f (θ)$ in the $θ - r$ -plane be used to provide information about the graph of the same equation in the polar plane?

Short Answer

Step by step solution

Step 1. Given information

Step 2.

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Most popular questions from this chapter

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How can the graph of an equation r=f(θ) in the θ-r-plane be used to provide information about the graph of the same equation in the polar plane?

Short Answer

Step by step solution

Step 1. Given information

Step 2.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Decision Maths

Geometry

Discrete Mathematics

Probability and Statistics

Study anywhere. Anytime. Across all devices.

How can the graph of an equation $r = f (θ)$ in the $θ - r$ -plane be used to provide information about the graph of the same equation in the polar plane?