Answered: Compare the polar equation of the…

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN:9781305071742

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter8: Polar Coordinates And Parametric Equations

Section8.2: Graphs Of Polar Equations

Problem 66E

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Compare the polar equation of the circle r = 2 with its equation in rectangular coordinates. In which coordinate system is the equation simpler? Do the same for the equation of the four-leafed rose r = sin(2θ). Which coordinate system would you choose to study these curves? Compare the rectangular equation of the line y = 2 with its polar equation. In which coordinate system is the equation simpler? Which coordinate system would you choose to study lines?

System that uses coordinates to uniquely determine the position of points. The most common coordinate system is the Cartesian system, where points are given by distance along a horizontal x-axis and vertical y-axis from the origin. A polar coordinate system locates a point by its direction relative to a reference direction and its distance from a given point. In three dimensions, it leads to cylindrical and spherical coordinates.

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