Sine expressions are very useful in rigging a wide range of applications.
If anything has a repetitive form, it can probably be done using a sine function.
The basic form of a sine expression is
A*sin(wT+phi), where
A = amplitude of the wave (usually a user input)
w=frequency(usually a user input)
T = time node in Maya
phi = This is the shift in time that is used to add variation to the pattern. Anytime you want to break the perfect smooth cycle and introduce some randomness, the phi term and the amplitude terms play a vital role.
I found this other useful link online that documents more on the sine wave.
I have not done many things with the sine wave, but enough to understand its potential. You could even script out a walk cycle maybe. but that would be more complicated than these simple examples here:
ferris Wheel example
curtain example
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