Why Does a Polar Plot of a Circle Only Show One Side of the Unit Circle?

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Discussion Overview

The discussion revolves around the behavior of polar plots, specifically why plotting a circle using the angle range from ##\theta \in [\pi/2, -\pi/2]## results in only the right side of the unit circle being displayed. The focus is on understanding the implications of angle ranges in polar coordinates.

Discussion Character

  • Technical explanation

Main Points Raised

  • One participant questions why the polar plot from ##\theta \in [\pi/2, -\pi/2]## only shows the right side of the unit circle, suggesting an expectation to see the left side as well.
  • Another participant clarifies that the plot is correct, explaining that ##\theta = 0## corresponds to the positive ##x##-axis, which is included in the specified range, while ##\theta = \pi##, corresponding to the negative ##x##-axis, is not included.
  • A third participant reiterates the initial question and adds that since ##\theta = 0## is within the range from ##\pi/2## to ##-\pi/2##, it leads to the expectation of displaying the side of the circle that contains 0. They suggest that a different range, ##\pi/2## to ##3\pi/2##, would be necessary to show the left side of the circle.
  • A later reply expresses understanding and appreciation for the explanation provided.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the initial question, but there is agreement on the explanation regarding the inclusion of angles in the specified range affecting the plot outcome.

Contextual Notes

The discussion does not resolve the underlying assumptions about the interpretation of angle ranges in polar coordinates, nor does it address potential implications for other ranges or plotting methods.

member 428835
Why is it when I plot a circle from ##\theta \in [\pi/2,-\pi/2]## I get the right side of the unit circle:

PolarPlot[1, {\[Theta], \[Pi]/2, -\[Pi]/2}]

? Shouldn't I get the left side?
 
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No. It is perfectly in order. ##\theta = 0## is the positive ##x##-axis and is part of your plot. ##\theta = \pi## is the negative ##x##-axis and is not part of your plot.
 
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joshmccraney said:
Why is it when I plot a circle from ##\theta \in [\pi/2,-\pi/2]## I get the right side of the unit circle:

PolarPlot[1, {\[Theta], \[Pi]/2, -\[Pi]/2}]

? Shouldn't I get the left side?
Note that ##\theta=0## is in the range from ##\pi/2## to ##-\pi/2##, so you expect to get the side of the circle containing 0.

What you want is the range from ##\pi/2## to ##3\pi/2## which does not contain 0.
 
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Likes   Reactions: member 428835
this makes tons of sense, thanks!
 

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