Chapter 9: Q 47. (page 731)

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = \sin^{3} θ$

Short Answer

Expert verified

The required equation is ${(x^{2} + y^{2})}^{2} = y^{3}$ .

Step by step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r = \sin^{3} θ$

Step 2. Find the equation in rectangular coordinates.

$r = \sin^{3} θ r = {(\frac{y}{r})}^{3} [\frac{y}{r} = \sin θ] r = {\frac{y}{r^{3}}}^{3}$

Now cross multiply,

role="math" localid="1649325945189" $r^{4} = y^{3} {(\sqrt{x^{2} + y^{2}})}^{4} = y^{3} [r^{2} = x^{2} + y^{2} and r = \sqrt{x^{2} + y^{2}}] {(x^{2} + y^{2})}^{\frac{4}{2}} = y^{3} {(x^{2} + y^{2})}^{2} = y^{3}$

Therefore, the equation in rectangular coordinates is ${(x^{2} + y^{2})}^{2} = y^{3}$ .

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In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = \sin^{3} θ$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the equation in rectangular coordinates.

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In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.r=sin3θ

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

Logic and Functions

Calculus

Statistics

Geometry

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

In Exercises 32–47 convert the equations given in polar coordinates to rectangular coordinates.
$r = \sin^{3} θ$