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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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Calculus 2 / BC

Chapter 10

Parametric Equations and Polar Coordinates

Section 1

Curves Defined by Parametric Equations

Parametric Equations

Polar Coordinates

Oregon State University

Harvey Mudd College

Baylor University

Boston College

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.

01:59

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 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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