Converting Polar to Cartesian - Step by Step Guide

In summary, the speaker is returning to studying after a few years and is struggling with converting Polar to Cartesian. They request some basic examples and a step-by-step guide. Another person then explains the procedure for converting (r,theta) to (x,y) and the speaker finds it easier now.
  • #1
chap
2
0
I'm back studying after a couple of years out and have become a little rusty. currently learning about the J operator.

I have no problem converting Cartesian to Polar, but struggle to convert Polar to Cartesian. Some basic examples and a step by step guide would be appreciated.


Thank you in advance.
 
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  • #2
Given [itex](r,\theta )[/itex] you can get [itex](x,y)[/itex] by the following procedure:

[itex]x=r\cos(\theta)[/itex]
[itex]y=r\sin(\theta)[/itex]
 
  • #3
Simple now you've pointed it out.

Thanks, that helps a lot.
 
  • #4
chap said:
Simple now you've pointed it out.

Thanks, that helps a lot.

Easier than cartesian to polar, huh?
 
  • #5
I know, I was thinking the same thing. :rofl:
 

1. What is the purpose of converting polar to cartesian coordinates?

The purpose of converting polar coordinates to cartesian coordinates is to represent points in a two-dimensional space using a different coordinate system. This can be useful in certain mathematical and scientific calculations and can also help visualize and graph data more accurately.

2. How do I convert polar coordinates to cartesian coordinates?

To convert polar coordinates to cartesian coordinates, you can use the following formulas:
x = r * cos(theta)
y = r * sin(theta)
where r represents the distance from the origin and theta represents the angle from the positive x-axis. Simply plug in the values for r and theta into these equations to get the corresponding cartesian coordinates.

3. What is the difference between polar and cartesian coordinates?

Polar coordinates use a distance and angle from the origin to represent a point in a two-dimensional space, while cartesian coordinates use x and y coordinates to represent a point in the same space. Polar coordinates are useful for representing circular or curved shapes, while cartesian coordinates are better for representing straight lines and grids.

4. Can you provide an example of converting polar coordinates to cartesian coordinates?

Sure! Let's say we have a point with polar coordinates (5, 60°). Using the conversion formulas, we can find the corresponding cartesian coordinates by plugging in the values:
x = 5 * cos(60°) = 2.5
y = 5 * sin(60°) = 4.33
Therefore, the cartesian coordinates for this point would be (2.5, 4.33).

5. What are some common mistakes to avoid when converting polar to cartesian coordinates?

One common mistake is forgetting to convert the angle from degrees to radians. Make sure to use the appropriate conversion (radians = degrees * (pi/180)) before plugging the value into the conversion formulas. Another mistake is forgetting to consider the quadrant the point is located in, as this can affect the signs of the coordinates. Lastly, double check your calculations to avoid any simple math errors.

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