/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q 27. In Exercises 24鈥�31 find all po... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Q 27. (page 730)

In Exercises 24鈥�31 find all polar coordinate representations for the point given in rectangular coordinates.

0,2

Short Answer

Expert verified

The polar coordinates are -2,-蟺2+2办蟺and2,蟺2+2办蟺, for any integerk.

Step by step solution

01

Step 1. Given information.

The given rectangular coordinate is:

0,2

Herex=0andy=2.

02

Step 2. Find the value of r.

To find the value of r, use the formula r=x2+y2:

r=02+22r=0+4r=卤2

03

Step 3. Find the value of θ.

Use the formula tan胃=yx,

tan胃=yxthen胃=tan-1yx胃=tan-120胃=tan-1鈭�

胃=-蟺2,蟺2,3蟺2Sincetan蟺2=鈭�;tan3蟺2=鈭�

04

Step 4. Find the polar coordinates.

Take,r=-2,胃=-蟺2thenr,胃=-2,-蟺2

The coordinates ofr,胃are-2,-蟺2+2办蟺, for any integer k.


Now take r=2,胃=3蟺2thenr,胃=2,3蟺2,

The coordinates of r,胃are2,蟺2+2办蟺, for any integer k.


Therefore, all the polar coordinates are-2,-蟺2+2办蟺and2,蟺2+2办蟺,

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 91影视!

One App. One Place for Learning.

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

Get started for free

Most popular questions from this chapter

Use Cartesian coordinates to express the equations for the hyperbolas determined by the conditions specified in Exercises 38鈥�43.

foci(卤2,0), directricesx=卤1

Use Cartesian coordinates to express the equations for the parabolas determined by the conditions specified in Exercises 22鈥�31.

r=伪1+cos胃

Use polar coordinates to graph the conics in Exercises 44鈥�51.

r=22+sin胃

Use Cartesian coordinates to express the equations for the ellipses determined by the conditions specified in Exercises 32鈥�37.

foci(卤1,0),major axis4

Each of the integral in exercise 38-44 represents the area of a region in a plane use polar coordinates to sketch the region and evaluate the expression

The integral is鈭�0蟺(1+cos胃)2d胃
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

Read Explanation

Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.