Exploring the Behavior of r=abs(sin n theta)

In summary, the equation for exploring the behavior of r=abs(sin n theta) is r = |sin(nθ)|, where r represents the distance from the origin and θ represents the angle in radians. The absolute value in the equation represents the distance from the origin, and changing the value of n affects the number of "petals" in the graph. The range of the graph for r=abs(sin n theta) is between 0 and 1, and this equation can be applied in real life to study circular patterns and in signal and image processing.
  • #1
vvc531
6
0

Homework Statement



Describe the behavior of
r= abs(sin n theta)
where n is a positive integer

Homework Equations



N/A

The Attempt at a Solution



I have no idea how to do this
 
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  • #2
What does the graph of y = sin(n[itex]\theta[/itex]) look like in comparison to the graph of y = sin([itex]\theta[/itex])

Now what does the graph of y = |sin(n[itex]\theta[/itex])| look like?
 
  • #3
I have done what u told me
However, i cannot come up with a good explanation to summarize the phenomena
 
  • #4
How about just describing the graph you got (the one for y = |sin(n[itex]\theta[/itex])|?
 

1. What is the equation for "Exploring the Behavior of r=abs(sin n theta)"?

The equation is r = |sin(nθ)|, where r represents the distance from the origin and θ represents the angle in radians.

2. What does the absolute value in the equation represent?

The absolute value in the equation represents the distance from the origin, which means that the graph will only show positive values for r.

3. How does changing the value of n affect the graph?

Changing the value of n changes the number of "petals" in the graph. For example, if n is 2, there will be 2 "petals" in the graph, and if n is 4, there will be 4 "petals".

4. What is the range of the graph for r=abs(sin n theta)?

The range of the graph for r=abs(sin n theta) is between 0 and 1, since the absolute value will always result in a positive value for r.

5. How can this equation be applied in real life?

This equation can be applied in real life to study the behavior of circular patterns, such as the growth of plants or the motion of objects in circular paths. It can also be used in signal processing and image processing to analyze and manipulate circular patterns.

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