Chapter 9: Q 45. (page 731)

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

Short Answer

Expert verified

The required equation is $y = \tan \sqrt{x^{2} + y^{2}}$ .

Step by step solution

Step 1. Given information.

The given equation in polar coordinates is:

$r = θ$

Step 2. Find the equation in rectangular coordinates.

$r = θ$

Substitute $r = \sqrt{x^{2} + y^{2}} and θ = \tan^{- 1} (\frac{y}{x})$

$\sqrt{x^{2} + y^{2}} = \tan^{- 1} (\frac{y}{x}) \tan \sqrt{x^{2} + y^{2}} = \frac{y}{x} x \tan \sqrt{x^{2} + y^{2}} = y y = \tan \sqrt{x^{2} + y^{2}}$

Therefore, the equation in rectangular coordinates is $y = \tan \sqrt{x^{2} + y^{2}}$ .

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

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

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

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

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

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

Pure Maths

Mechanics Maths

Theoretical and Mathematical Physics

Applied Mathematics

Calculus

Decision Maths

Study anywhere. Anytime. Across all devices.

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