Why is there this pattern in the polar curves cos[at] U sin[at]

  • Thread starter Thread starter flyingpig
  • Start date Start date
  • Tags Tags
    Curves Polar
Click For Summary

Homework Help Overview

The discussion revolves around the polar plots of functions involving sine and cosine, specifically examining the patterns in the number of loops generated by these functions as the frequency of the angle variable increases. The original poster presents a series of polar equations and notes an interesting relationship between the frequency and the resulting number of loops.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the frequency of the angle variable and the number of loops in the polar plots. Some question the visibility of the loops when using odd multiples of the angle, while others suggest that the graph is plotted multiple times.

Discussion Status

The discussion is ongoing, with participants offering different interpretations of the observed patterns. There is a divergence in understanding regarding the visibility and representation of loops in the polar plots, indicating a productive exploration of the topic.

Contextual Notes

Participants are considering the implications of plotting from 0 to pi and how this affects the perceived number of loops in the graphs. There is also a mention of the original poster's observations about the doubling of loops for even multiples versus the consistency for odd multiples.

flyingpig
Messages
2,574
Reaction score
1

Homework Statement



Polar plot the following

sin[t] U cos[t]
sin[2t] U cos[2t]
sin[3t] U cos[3t]
sin[4t] U cos[4t]
sin[5t] U cos[5t]

Notice that cos[t] and sin[t] are the same graph rotated 90 degrees only? Interesting! Just like the cartesian graph.

Now here is something more interesting

The number of loops follow as

1t U 1 loop
2t U 4 loops
3t U 3 loops
4t U 8 loops
5t U 5 loop

Notice how the odd number stays the same and the even doubles? Why is there this pattern?
 
Physics news on Phys.org
They actually have the same number of loops. When you use the odd multiple of t the graph is plotted twice. Try going from 0 to pi.
 
But you can't see it! So it is halved.
 
flyingpig said:
But you can't see it! So it is halved.

Believe whatever you want to.
 

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
Replies
3
Views
1K
  • · Replies 1 ·
Replies
1
Views
9K
Replies
8
Views
2K
Replies
1
Views
3K
  • · Replies 7 ·
Replies
7
Views
15K
  • · Replies 4 ·
Replies
4
Views
2K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 12 ·
Replies
12
Views
5K
  • · Replies 7 ·
Replies
7
Views
2K