Understanding Polar and Cartesian Graphs: Comparing Two Coordinate Systems

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Discussion Overview

The discussion centers around the comparison of polar and Cartesian coordinate systems, specifically in the context of graphing trigonometric functions. Participants explore whether the graphs in these two systems represent the same underlying function.

Discussion Character

  • Conceptual clarification
  • Exploratory

Main Points Raised

  • One participant notes that there are two ways to graph a trigonometric function: in the Cartesian Coordinate Plane with (x,y) values and in the Polar Coordinate system with (r,θ) values.
  • Another participant asserts that both graphs represent the same function and have the same values when the coordinate system is converted.
  • A participant expresses gratitude for the clarification provided.
  • One participant mentions that polar coordinates are confusing.
  • A participant indicates they are just starting to learn about polar coordinates and anticipates having questions later.

Areas of Agreement / Disagreement

Participants generally agree that both coordinate systems can represent the same function, but there is no detailed exploration of the nuances or complexities involved in the conversion between the two systems.

Contextual Notes

There may be limitations in understanding the conversion process between coordinate systems, as well as potential confusion regarding the representation of functions in polar coordinates.

opus
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Please see the attached image.
To my understanding, there are two ways to graph a trigonometric function.
One is in the Cartesian Coordinate Plane where we have the values (x,y).
The other is in the Polar Coordinate system where we have the values (r,θ).

In regards to the image that I've attached, are these graphs saying the same thing, just in different coordinate systems?
 

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Yes, both the graphs are representing the same function and have the same values if you will convert the coordinate system.
 
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Great thank you.
 
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Your welcome. Anyway, polar coords are confusing
 
Just starting learning about them, so I'm sure I'll have questions later.
 

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