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Graphs of Polar Equations Calculator

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Example
Created on 2024-06-20Asked by Levi Scott (Solvelet student)
Sketch the graph of the polar equation r=1+cos(θ) r = 1 + \cos(\theta) .

Solution

To sketch the graph of the polar equation r=1+cos(θ) r = 1 + \cos(\theta) : The equation r=1+cos(θ) r = 1 + \cos(\theta) represents a limaçon. To plot it, we use the following table of values: \begin{array}{|c|c|} \hline \theta & r = 1 + \cos(\theta) \ \hline 0 & 2 \ \frac{\pi}{2} & 1 \ \pi & 0 \ \frac{3\pi}{2} & 1 \ 2\pi & 2 \ \hline \end{array} \begin{center} \begin{tikzpicture} \begin{polaraxis}[grid=both] \addplot coordinates { (0,2) (90,1) (180,0) (270,1) (360,2) }; \end{polaraxis} \end{tikzpicture} \end{center} The graph is a limaçon with an inner loop. Solved on Solvelet with Basic AI Model
Some of the related questions asked by Logan Hall on Solvelet
1. Plot the graph of the polar equation r=2+3sin(θ)r = 2 + 3\sin(\theta),2. Identify the polar equation that represents the cardioid with the polar equation r=1cos(θ)r = 1 - \cos(\theta).,
DefinitionPolar equations graphs the relationship between two variables in the polar coordinate system, where points are determined by a distance and an angle with respect to a fixed point (the pole). The polar coordinate system is particularly well-suited to graphing certain types of curves that are more very difficult to graph in a standard coordinate system, such as spirals, circles, and roses. As a result, polar splits are widespread in physics, engineering, and graphics, where they are generally used to represent oscillatory or rotational phenomena. For example, the polar equation r=1+sin(θ) is the limaçon, a type of polar curve that has loops and petals.
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