Pat, you are absolutely correct in your interpretation of non-rotation of , but I think the oscillation perspective is valid.

Think of as the center line for . Then the final graph is exactly 1 unit above the center line at , is on the center line at , is one below the center line at , returns to the center line at , and returns to 1 unit above at . This behavior is confirmed by the graph, showing that the oscillation in this case is entirely VERTICAL, as one would expect from a Cartesian function. From this perspective, indeed is a standard cosine graph oscillating around .

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