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

$ x = 5\sin t $, $ \; y = 2\cos t $, $ \; -\pi \leqslant t \leqslant 5\pi $

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$x=5 \sin t, y=2 \cos t \Rightarrow \sin t=\frac{x}{5}, \cos t=\frac{y}{2} \cdot \sin ^{2} t+\cos ^{2} t=1 \Rightarrow\left(\frac{x}{5}\right)^{2}+\left(\frac{y}{2}\right)^{2}=1 .$ The motion of theparticle takes place on an ellipse centered at $(0,0) .$ As $t$ goes from $-\pi$ to $5 \pi,$ the particle starts at the point (0,-2) and movesclockwise around the ellipse 3 times.

Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Missouri State University

Campbell University

Harvey Mudd College

Idaho State University

Lectures

16:57

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.

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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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Describe the motion of a p…

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the problem isthe describes a motion for particle with tradition acts. Why asked worries in given into war First half ax over five squire us fly over. She was squire. It's equal to one. This is on your lips and we can sketch the graph as follows. It is a negative five Far negative two hundred two on day one. He is too negative. Pie, We have axe to zero. Why you go to negative two zero Negative too. So this pond Monty is a go to zero. We're half axe. Go to zero. And why he called you too. Auntie is equal to negative high over too. Accessing a connective off. Why secret with Cyril? Over half my anti virus, from neck to pie to pie. So article goes from this point in this direction on DH back to this point. This is what she virus from neck to try to find the particle. Because from this point, this direction back to this point. And then I want to last two high two three pie. So the particle goes from this point in this direction on DH, then back to this point. Andi, want tea? Last two three pie to file pie. The particle goes from this point, this direction and back to this point

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