Solution Found!

Calculus / Calculus: Early Transcendentals 1 / Chapter 10.1 / Problem 16E

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Change Question

Solved: Circles and arcs Eliminate the parameter to find a

Chapter 8, Problem 16E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Eliminate the parameter to find a description of the following circles or circular arcs in terms of x and y. Give the center and radius, and indicate the positive orientation.

\(x=3 \cos t,\ y=3 \sin t;\ 0\ \leq\ t\ \leq\ \pi/2\)

Questions & Answers

QUESTION:

Eliminate the parameter to find a description of the following circles or circular arcs in terms of x and y. Give the center and radius, and indicate the positive orientation.

\(x=3 \cos t,\ y=3 \sin t;\ 0\ \leq\ t\ \leq\ \pi/2\)

ANSWER:

Solution 16E

Step 1:

In this problem we have to eliminate the parameter o find a description of the following circles or circular arcs in terms of x and y.

Given $x=3\ cos\ t,\ y=3\ sin\ t$

This is very similar to the circle of radius 3.

Now suppose we plug in these parametric equations to ${x}^{2}+{y}^{2}$ we get

$(3cos\ t{)}^{2}+(3\ sin\ t{)}^{2}={3}^{2}co{s}^{2}t+{3}^{2}si{n}^{2}t={3}^{2}(co{s}^{2}t\ +\ si{n}^{2}t)={3}^{2}$

(since $co{s}^{2}t+si{n}^{2}t=1)$

Thus ${x}^{2}+{y}^{2}={3}^{2}$

$\Rightarrow{}{x}^{2}+{y}^{2}=9$

This is a circle of radius 3, centered at (0, 0).

Study Tools You Might Need

Chapter: 2 Problem: 112P

Introductory Chemistry 5
A backpacker carries 2.5 L of white gas as fuel for her stove. How many pounds does the fuel add to her load? Assume the density of white gas to be \(0.79\mathrm{\ g}/\mathrm{cm}^3\).

Chapter: 5 Problem: 79P

Introductory Chemistry 5
Name each acid. (a) HClO (b) \(\mathrm{HClO}_{2}\) (c) \(\mathrm{HClO}_{3}\) (d) \(\mathrm{HClO}_{4}\) Equation Transcription: Text Transcription: HClO_2 HClO_3 HClO_4

Chapter: 14 Problem: 17Q

Introductory Chemistry 5
What is the difference between a strong acid and a weak acid?

Chapter: 6 Problem: 124CQ

General, Organic, and Biological Chemistry: Structures of Life 4
Problem 124CQ A toothpaste contains 0.24% by mass sodium fluoride (NaF) used to prevent dental caries and 0.30% by mass triclosan, C12H7Cl3O2, a preservative and antigingivitis agent. One tube contains 119 g of toothpaste. (6.4, 6.5) Components in toothpaste include triclosan and NaF. a. How many

Chapter: 3 Problem: 3.63

Physics for Scientists and Engineers: A Strategic Approach, Standard Edition (Chs 1-36) 4
Dee is on a swing in the playground. The chains are 2.5 m long, and the tension in each chain is 450 N when Dee is 55 cm above the lowest point of her swing. Tension is a vector directed along the chain, measured in newtons, abbreviated N. What are the horizontal and vertical components of the tensio

Chapter: 3 Problem: 3.7

Organic Chemistry, 9
Given the following partial structure, add a substituent X to C-1 so that it satisfies the indicated stereochemical requirement What is the ACCX torsion (dihedral) angle in each? (a) Anti to A (c) Anti to C-3 A 3 1 (b) Gauche to A (d) Gauche to C-3

Chapter: 11 Problem: 3

Campbell Biology 10
. Lipid-soluble signaling molecules, such as aldosterone, cross the membranes of all cells but affect only target cells because a. only target cells retain the appropriate DNA segments. b. intracellular receptors are present only in target cells. c. only target cells have enzymes that break down aldo

Chapter: 2 Problem: 1

General Chemistry. Principles and Modern Applications 11
When an iron object rusts, its mass increases. When a match burns, its mass decreases. Do these observations violate the law of conservation of mass? Explain.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account