by: Tim Lehman
Write-Up #11
For this writeup, we are studying polar cordinates. We will inspect
r=2a sin(k
) +b
and r=2a cos(k
) for various values of a, b, and
k. To start, we will vary one of the three variables a, b, and
k and hold each of the other two variables constant.
)
+bWe will first examine the effect on the graph by holding k at 1, b at zero, and varying a.
For an idea what this looks like, check out this movie.
Next, we will hold a=1, b=0, and look at different values for k. A movie of this graph is available here.
Lastly, we study the graph when a=1, k=1, and
b varies. For a graph of this when b changes from -10 to 10, click here.
)+bWe will first examine the effect on the graph by holding k at 1, b at zero, and varying a.
For an idea what this looks like, check out this movie.
Next, we will hold a=1, b=0, and look at different values for k. A movie of this graph is available here.
Lastly, we study the graph when a=1, k=1, and b varies. For a graph of this when b changes from -10 to 10, click here.