Find a polar equation for the curve represented by the given Cartesian equation: 4x + 2y = 4

Question:

Find a polar equation for the curve represented by the given Cartesian equation:

4x + 2y = 4

Polar coordinate system

The most common method of mapping a certain point into the two-dimensional space is by using the Cartesian coordinate plane. This coordinate plane uses the horizontal and vertical distance of the point from a fixed reference point in the center, called the origin. However, there is another means of plotting points in a plane. The polar coordinate system utilizes the distance of the point from another fixed reference point and an angle to indicate direction. The distance from the fixed reference point called the pole is called radius or the radial coordinate, usually denoted by {eq}r {/eq}. The angle is called the angular coordinate, and it is usually denoted as {eq}\theta {/eq}.

If the Cartesian coordinate plane is made up of the intersections of vertical and horizontal lines, the polar coordinate system is made up of concentric circles (or varying radii) seemingly emanating from the central point (the pole).

Answer and Explanation: 1

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Recall the following equations used in converting Cartesian equations to polar form

{eq}x=r\cos\theta \\ y=r\sin\theta {/eq}

The given Cartesian...

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Graphing Functions in Polar Coordinates: Process & Examples

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Chapter 24 / Lesson 1
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Learn how to graph polar equations and plot polar coordinates. See examples of graphing polar equations. Transform polar to rectangular coordinates and vice versa.


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