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Function riding on another function

by preposterous
Tags: function, riding
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preposterous
#1
Jan29-13, 12:14 AM
P: 3
How do I write sin(x) where the x-axis is a function itself. For example, I want to write sin(x) along a half circle. I need to "wrap" the function, similar to "De Broglie wavelength" in image below.

More specifically, I want to write f1 = 0.1*sin(x) the where the x-axis is f2 = sqrt(10^2 - x^2).

I know that this generally will not pass the vertical line test. But for my application it will becuase the sin(x) has small amplitude compared to the circle radius.
Attached Thumbnails
deBroglie_E.jpg  
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chiro
#2
Jan29-13, 01:11 AM
P: 4,572
Hey preposterous.

One example like the diagram in your post would be in polar co-ordinates:

r = 1 + 0.5*cos(theta)

where in cartesian co-ordinates you use the relationship:

r^2 = x^2 + y^2 and

tan(theta) = y/x
rollingstein
#3
Jan29-13, 04:18 AM
PF Gold
P: 330
Why not

0.1 * sin(sqrt(10^2 - x^2))


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