Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

Find all polar coordinates that represent the point (1,0)given in rectangular coordinates.

Short Answer

Expert verified

The polar coordinates are (-1,(2k+1)π),(1,2kπ), for any integer k

Step by step solution

01

Given information

The rectangular coordinate (1,0).

02

Simplification

Consider the rectangular coordinate (1,0).

The objective is to convert the rectangular coordinates to polar coordinates.

In the coordinate (1,0),x=1and y=0.

To find the value of ruse the equation r=x2+y2.

Then,

r=x2+y2r=(1)2+(0)2[sincex=1,y=0]r=±1

To calculate θuse the formula θ=tan-1yx.

By substituting x,yin the formula,

θ=tan-101[sincex=1,y=0]θ=tan-1(0)θ=π,2π[sincetanπ=tan2π=0]

Take r=-1,θ=π

Then (r,θ)=(-1,π)

Thus, the coordinates of (r,θ)are(-1,(2k+1)π), for any integer k.

Now take r=1,θ=2π

Then (r,θ)=(1,2π).

The coordinates of (r,θ)are (1,2kπ),for any integer k.

Therefore, the polar coordinates are (-1,(2k+1)π),(1,2kπ), 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.

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

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Study anywhere. Anytime. Across all devices.

Sign-up for free