Answered: Compare the equation r=2 with its…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.6: Parametric Equations

Problem 2ECP

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Compare the equation r=2 with its equation in rectangler coordinates. In which coordinate system is the equation simpler? Do the same for the equation of the four leafed rose r=sin 20. Which coordinate system would you choose to study these curves?

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.

Expert Solution

Step 1

The given equation is $r = 2$ .

Square both sides of the equation.

$\begin{array}{rcl} r^{2} & = & 2^{2} \\ = & 4 \end{array}$

Substitute 4 for r² in the equation $x^{2} + y^{2} = r^{2}$ .

$x^{2} + y^{2} = 4$

Thus, the equation in rectangular coordinates is $x^{2} + y^{2} = 4$ .

The equation is much more simpler in polar coordinates.

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