Two young mathematicians think about periodic motion.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Hey Riley, what is that?
Riley
I hooked a weak spring to the bottom of this shelf, then hung a pen on it. I’m watching the pen bounce up and down.
Devyn
Sure, I can see that.
Riley
See how the pen starts down at the bottom, bounces up to the top, then back to the bottom again?
Devyn
Yeah. It’s just repeating that same pattern over and over again.
Riley
I graphed the height of that pen, with respect to time. Here’s what I found.
Devyn
Hey, that looks familiar!
Devyn and Riley have discovered simple harmonic motion. What function did Riley plot?
Since we’re talking about trigonometric functions, we have to be very clear about our units. What units do we use to measure angles / rotation when we see an expression like ?
Only degrees. Usually degrees, but occasionally radians. Occasionally degrees, but usually radians. Only radians.