Chapter 9: Q 24. (page 730)

In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
$(0, 0)$

Short Answer

Expert verified

The polar coordinates are $(0, (2 k + 1) π) and (0, 2 kπ)$ , for any integerk.

Step by step solution

Step 1. Given information.

The given rectangular coordinate is:

$(0, 0)$

Here $x = 0 and y = 0$ .

Step 2. Find the value of r.

To find the value of r, use the formula $r^{2} = x^{2} + y^{2}$ :

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(0)}^{2} + {(0)}^{2}} r = \sqrt{0} r = 0$

Step 3. Find the value of θ.

Use the formula $\tan θ = \frac{y}{x}$ ,

localid="1649227271585" $\tan θ = \frac{y}{x} θ = \tan^{- 1} (\frac{y}{x}) θ = \tan^{- 1} (\frac{0}{0}) θ = \tan^{- 1} (0)$

$θ = 0, π, 2 π$ localid="1649227391599" $(Since \tan 2 π = 0; \tan π = 0)$ )

Step 4. Find the polar coordinates.

Now take $r = 0, θ = π$ ,

Then $(r, θ) = (0, π)$

The coordinates will become localid="1649227976138" $(0, (2 k + 1) π) and (0, 2 kπ)$ for any integer k.

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 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
$(0, 0)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of r.

Step 3. Find the value of θ.

Step 4. Find the polar coordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Mechanics Maths

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.0,0

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the value of r.

Step 3. Find the value of θ.

Step 4. Find the polar coordinates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Applied Mathematics

Mechanics Maths

Geometry

Statistics

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Exercises 24–31 find all polar coordinate representations for the point given in rectangular coordinates.
$(0, 0)$