Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Sent to:
Search glass icon
  • Login
  • Textbooks
  • Ask our Educators
  • Study Tools
    Study Groups Bootcamps Quizzes AI Tutor iOS Student App Android Student App StudyParty
  • For Educators
    Become an educator Educator app for iPad Our educators
  • For Schools

Question

Answered step-by-step

Problem 52 Hard Difficulty

Investigate the family of curves defined by the parametric equations $ x = \cos t $, $ y = \sin t - \sin ct $, where $ c > 0 $. Start by letting $ c $ be a positive integer and see what happens to the shape as $ c $ increases. Then explode some of the possibilities that occur when $ c $ is a fraction.


Video Answer

Solved by verified expert

preview
Numerade Logo

This problem has been solved!

Try Numerade free for 7 days

WZ
Wen Zheng
Numerade Educator

Like

Report

Textbook Answer

Official textbook answer

Video by Wen Zheng

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Related Topics

Parametric Equations

Polar Coordinates

Discussion

You must be signed in to discuss.
Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

16:57

Graphing

In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.

Video Thumbnail

01:59

Polar Coordinates - Intro

Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).

Join Course
Recommended Videos

02:02

Investigate the family of …

04:35

$$ \begin{array}{l}{\text …

01:03

Investigate the family of …

02:24

Investigate the family of …

02:05

Investigate the family of …

01:15

Investigate the family of …

01:45

Investigate the family of …

01:11

Investigate the family of …

Watch More Solved Questions in Chapter 10

Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
Problem 30
Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
Problem 41
Problem 42
Problem 43
Problem 44
Problem 45
Problem 46
Problem 47
Problem 48
Problem 49
Problem 50
Problem 51
Problem 52

Video Transcript

the problem is investigated. The family off curves did find the bus. Parametric equations actually put this society while going to sign the minus sign stayed home steam wire seasick with his and cereal. Start by light and save your positive integer on DH. Say what happens to the ship at sea increases. They explored some of the possibilities that our care What C is a fraction. Look at this graph. Here I see a single one. The curve is a line segment. I say you got to. It's a curve into a sex itself. At one point, my C is equal to three. Curve intersects itself at two points. Must see is it four? The curve intersects itself at three points so we can guess. For safe go to some in and this positive interview the curve intersects the south at a month. One points. Then let's look at some examples. What sees a fraction. If the denominator is equal to three we have. That's a look at this example. If sees it, criticism. One on the denominator is equal to three. Your half the curve dissects itself at fifteen points. It says he got a four one three Andi. If sees you go too far over three, the curve in the sects itself. All right, eighteen points and over half. But if the denominator is not equal to three point damn point if this is too, we have if this is seven over too, the curve in just sects in the south at their team points.

Get More Help with this Textbook
James Stewart

Calculus: Early Transcendentals

View More Answers From This Book

Find Another Textbook

Study Groups
Study with other students and unlock Numerade solutions for free.
Math (Geometry, Algebra I and II) with Nancy
Arrow icon
Participants icon
178
Hosted by: Ay?Enur Çal???R
Math (Algebra 2 & AP Calculus AB) with Yovanny
Arrow icon
Participants icon
75
Hosted by: Alonso M
See More

Related Topics

Parametric Equations

Polar Coordinates

Top Calculus 2 / BC Educators
Anna Marie Vagnozzi

Campbell University

Kayleah Tsai

Harvey Mudd College

Samuel Hannah

University of Nottingham

Joseph Lentino

Boston College

Calculus 2 / BC Courses

Lectures

Video Thumbnail

16:57

Graphing

In mathematics, a graph is a representation of a set of objects where some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called "vertices" or "nodes", and the relations between them are represented by mathematical abstractions called "edges" or "arcs". The basic notion of a graph was developed by the 17th-century French mathematician Pierre de Fermat, and the term "graph" was coined by the 19th-century mathematician James Joseph Sylvester. The more general mathematical concept of a graph "in which any kind of relation between elements of the set is expressed as an edge, is called a network" (Kolmogorov, "1956, p. 111"). In other words, an undirected graph is a graph in which the edges have no direction associated with them. The most familiar examples of graphs are the graphs of equations. In general, the vertices of a graph can represent concepts and the edges can represent real-valued functions on the concepts, so one can speak of the graph as a function's graph or of the edge as a function's edge.

Video Thumbnail

01:59

Polar Coordinates - Intro

Polar coordinates are a two-dimensional coordinate system that specifies a point in terms of distance from a reference direction (the pole) and angle from a reference direction (the polar axis).

Join Course
Recommended Videos

02:02

Investigate the family of curves defined by the parametric equations $x=\cos t…

04:35

$$ \begin{array}{l}{\text { Investigate the family of curves defined by the par…

01:03

Investigate the family of curves defined by the parametric equations $ x = t^2 …

02:24

Investigate the family of curves given by the parametric equations $x=t^{3}-c t…

02:05

Investigate the family of curves given by $f(x)=x-c \sin ^{-1} x .$ What happe…

01:15

Investigate the family of curves defined by the parametric equations $x=t^{2},…

01:45

Investigate the family of curves defined by the parametric equations $x=t^{2},…

01:11

Investigate the family of curves given by $f(x)=x e^{-c x},$ where $c$ is a rea…
Additional Mathematics Questions

01:06

'Pakisagot po ito thnks
+Brainliest
+likes
+rate5/5
Aned e…

02:12

"pano po gagawin at ano po sagot dyan
Answer Me, Color Mel Dirctona …

01:46

'How many ways can 3 female students and 4 male students be seated on a…

02:49

'please answer the math problem
(y ulp I2 + ATw [V'

04:22

'Pa tulong po ako please kailangan ko po talaga
discussion above, fi…

01:12

'3 Po please please please
acup 0f batler Ai lo make spatcake mix ad…

03:34

'Solve the following words problems.
The area of Ihe rectangle rect…

05:12

'Complete the following table
D Learning Task 1: notebook: Complete…

02:01

'1) 50 is 8% of whatnumber?
Learning Task 2: Find the base. Write yo…

03:25

'learning task 2 translate the following sentence.Use x to represent nu…

Add To Playlist

Hmmm, doesn't seem like you have any playlists. Please add your first playlist.

Create a New Playlist

`

Share Question

Copy Link

OR

Enter Friends' Emails

Report Question

Get 24/7 study help with our app

 

Available on iOS and Android

About
  • Our Story
  • Careers
  • Our Educators
  • Numerade Blog
Browse
  • Bootcamps
  • Books
  • Notes & Exams NEW
  • Topics
  • Test Prep
  • Ask Directory
  • Online Tutors
  • Tutors Near Me
Support
  • Help
  • Privacy Policy
  • Terms of Service
Get started