For injecting some why-you-might-ever-care-about-this juice into your trigonometric graphing:
In this one the good part starts around 0:08, then again in the final seconds -
Plan - show one clip or both. What are we looking at here? What are the features of the motion? What words would you use to describe it? How might you compare one swimmer's kick with another's? What attributes might you try changing to improve a kick? How does the sun's path differ at other times of the year? At other latitudes? How is it the same? Generally keep poking at it until we describe it as periodic, and mention synonyms for amplitude and frequency. Proceed as usual.
Later in the unit, project a still of the kick trail, and write an equation for it.
If anyone's got other clips of periodic motion bookmarked or favorited, I'd love to see them.