Thank you, GaryB! You just posted Exhibit A of the most misunderstood aspect of a "pause" -- that if something stops and changes direction, that in itself "must be a pause." It isn't. Just because something comes to a stop and changes direction, doesn't mean that in itself "is a pause." Here's why...
When you throw a ball straight up into the air, yes, it will slow down, come to a stop, and begin falling to the earth. But the point at which that ball is "stopped" in mid-air is INSTANTANEOUS. There is no "hang time" where the ball stays motionless in mid-air for a measurable period of time. The moment that balls stops, it begins to fall back to earth instantaneously. It may look to your human eye as the ball "pausing" there in mid-air, but rest assured, it isn't.
The same thing with a child swinging on a swing, or with a sinusoidal (sine) wave. That sine wave, when rising and falling, is continuously slowing down, coming to a stop, and changing direction. Yet there is NEVER a pause in this motion. To put a pause in a child's swing, somebody has to grab it and hold it, and then let it go. To put a pause in a sine wave, you have to clip the tops of that sine wave's peaks off (giving them a "flat-top haircut" so-to-speak), thereby making it no longer a sine wave, but making it more resemble a square wave.
I hope that helps,
-Sean