Chapter 9: Q. 63 (page 568)

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(1.3, - 2.1)$

Short Answer

Expert verified

The polar coordinates is $(2.47, - 1.02)$ .

Step by step solution

Step 1. Given Information

We are given rectangular coordinates of a point,

$(1.3, - 2.1)$

We have to find polar coordinates of given point.

Step 2. Finding the polar coordinates

The distance of the point $(1.3, - 2.1)$ from origin is given by,

$r = \sqrt{x^{2} + y^{2}} r = \sqrt{{(1.3)}^{2} + {(- 2.1)}^{2}} = \sqrt{1.69 + 4.41} = \sqrt{6.1} = 2.47$

Step 3. Finding the polar coordinates

We know that,

$\tan θ = \frac{y}{x}, so θ = \tan^{- 1} \frac{y}{x}, - \frac{π}{2} < θ < \frac{π}{2}$

Putting values, we get

$θ = \tan^{- 1} (\frac{- 2.1}{1.3}) = \tan^{- 1} (- 1.615) = - 1.02$

So, the polar coordinate will be $(2.47, - 1.02)$ .

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 Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(1.3, - 2.1)$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the polar coordinates

Step 3. Finding the polar coordinates

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Applied Mathematics

Decision Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point. 1.3,-2.1

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Finding the polar coordinates

Step 3. Finding the polar coordinates

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Discrete Mathematics

Applied Mathematics

Decision Maths

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

In Problems55–66, the rectangular coordinates of a point are given. Find polar coordinates for each point.
$(1.3, - 2.1)$