How to compose sin(x) with a curved path like a semicircle

[preposterous]

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 because the sin(x) has small amplitude compared to the circle radius.

 

[chiro]

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]

Why not

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