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Sketch the curve by using the parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as $ t $ increases.
$ x = t + \sin t $, $ \quad y = \cos t $, $ \quad -\pi \leqslant t \leqslant \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
Missouri State University
Harvey Mudd College
University of Michigan - Ann Arbor
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.
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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Sketch the curve by using …
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The problem is sketch a curve by using the parametric equations to plot points indicate with an arrow the direction in which the curve is traced, as t increases. So first we compute the values of x and y and t is equal to negative pi x is equal to negative pi y is equal to negative 1 point and p is equal to negative pi. Over 2 half x is equal to negative pi over 2 minus 1 point y is equal to 0 point. When t is equal to 0 x is equal to 0 y is equal to y and t is equal to pi. Over 2 x is equal to pi. Over 2 plus 1 point y is equal to 0 point, and t is equal to pi. We have x is equal to pi as 0, so this is pi and y is equal to negative 1 point. Now, let's get the curve. First negative desis negative pi over 2 and negative pi pi over 2 and pix. I go to negative pi y is equal to negative 1, so negative, 10 and 1. I negative pi negative 1, so here and negative pi over 2 minus 1 is about here and 01, and here and here so the craft is like this. This is a curve by using the parametric equations to plot point and there's a direction. Arrow is a direction in which the curve is traced. Ses,
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