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Suppose a curve is a given by the parametric equa…

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Problem 22 Easy Difficulty

Describe the motion of a particle with position $ (x, y) $ as $ t $ varies in a given interval.

$ x = \sin t $, $ \; y = \cos^2 t $, $ \; -2\pi \leqslant t \leqslant 2\pi $


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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

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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).

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Watch More Solved Questions in Chapter 10

Problem 1
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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 thiss crabs emotional for particle West position X y as to worries enough given interval. So first to behalf. Explain us why it's Niko too. Cyril is equal to one. Then we can scratch the graph as follows. So first notice that why is Elvis greatest hero? Max is in between next to a one on one. So this is a graph when he is a connective too high Behalf X is equal to zero. Why? Because you why one? He is the co two negative dream high over to have axe. Is the coat too one wine too zero over half Once he worries from negative Too high two zero over half the particle goes from this point. So first too this point and then back to this point. And then because to this pond and then back to this point. And the one team wire is from Cyril and too hard to troop I There's a particle goes from this part too one zero and then back to one and then goes to elective one year old and then back to Sierra one

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Related Topics

Parametric Equations

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Top Calculus 2 / BC Educators
Heather Zimmers

Oregon State University

Kayleah Tsai

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Caleb Elmore

Baylor University

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
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