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Is there a term for the argument of the sine function outside of geometry?

Are there similar terms in other areas for the idea the "angle" conveys in geometry? I find that functions for abstract things such as pressure, electrical currents (nothing geometric there) on AC ...
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Does a cycle (in Simple Harmonic Motion) have to equal 2π?

So, I search for the definition of cycle and I get this in Wikipedia: A turn is a unit of angle measurement equal to 360° or 2π radians (or ...). A turn is also referred to as a revolution or ...