Understanding Polar and Cartesian Graphs: Comparing Two Coordinate Systems

In summary, there are two ways to graph a trigonometric function: in the Cartesian Coordinate Plane with values (x,y) or in the Polar Coordinate system with values (r,θ). The attached image shows two graphs representing the same function in different coordinate systems. Converting between the two systems will result in the same values. However, some find the polar coordinate system confusing and may have questions when first learning about it.
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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
 
  • #5
Just starting learning about them, so I'm sure I'll have questions later.
 

FAQ: Understanding Polar and Cartesian Graphs: Comparing Two Coordinate Systems

1. What is the difference between a polar and a Cartesian graph?

A polar graph is a type of graph that uses polar coordinates to plot data, while a Cartesian graph uses rectangular coordinates. In a polar graph, the distance from the origin and the angle from a reference line are used to locate points, while in a Cartesian graph, the x and y coordinates are used.

2. Which type of graph is better for representing circular data?

A polar graph is better for representing circular data because it uses angles to plot points, making it easier to visualize circles and other curved shapes.

3. Are there any limitations to using polar graphs?

Yes, one limitation of polar graphs is that they can only represent data in a two-dimensional space. This means they are not suitable for representing more complex data sets that require three or more dimensions.

4. How do you convert a polar graph to a Cartesian graph?

To convert a polar graph to a Cartesian graph, you can use the following equations:

x = r * cos(theta)

y = r * sin(theta)

where r is the distance from the origin and theta is the angle from the reference line. These equations will give you the corresponding x and y coordinates for each point on the polar graph.

5. Can you use both polar and Cartesian graphs together?

Yes, you can use both types of graphs together to represent different aspects of the same data. For example, you could use a polar graph to show the direction of movement and a Cartesian graph to show the magnitude of the movement.

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