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Chapter 9: Q 39. (page 731)

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = 6 \csc θ$

Short Answer

Expert verified

The required equation is $y = 6$ .

Step by step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r = 6 \csc θ$

Step 2. Find the equation in rectangular coordinates.

$r = 6 \csc θ r = 6 \cdot \frac{1}{\sin θ} r \sin θ = 6 y = 6 [Since r \sin θ = y]$

Therefore, the equation in rectangular coordinates is $y = 6$ .

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Most popular questions from this chapter

Find a definite integral expression that represents the area of the given region in polar plane and then find the exact value of the expression

The region inside the circle $x^{2} + y^{2} = 1 a n d r i g h t o f t h e v e r t i c a l l i n e x = \frac{1}{2}$

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 $r = 1 + 2 \sin θ$

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 $A = \int_{0}^{\frac{π}{2}} \sin 2 θ d θ$

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 $(- C, 0) is D_{2} = \frac{A^{2} + C x}{A^{2}}, where C = \sqrt{A^{2} - B^{2}} .$

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

$r = \frac{2}{1 - 3 \cos θ}$

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In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = 6 \csc θ$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

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Most popular questions from this chapter

Recommended explanations on Math Textbooks

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In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.r=6cscθ

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Probability and Statistics

Geometry

Calculus

Mechanics Maths

Pure Maths

Study anywhere. Anytime. Across all devices.

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = 6 \csc θ$