This time, treat the wave generated on the unit circle as a real function. Adjust the amplitude (a), the period multiplier b, the phase shift (h), and the vertical shift (d) one at a time and see how the graph changes.
As a point on the unit circle spins around, drawing out its vertical position continuously over time gives a wavy, undulating shape. This is exactly the graph of the sin function. cos and tan come from the same principle, but their starting points and shapes are each a little different.
Periodic waves like this show up all around us. The way sound spreads, the tide rising and falling twice a day, even the height of a Ferris wheel as it turns — all of these can be represented with trig function graphs.
The amplitude a determines how high and low the wave swings, b determines how long one repetition takes (the period), h determines how far the graph shifts left or right, and d determines how far it shifts up or down. Move each slider one at a time and see how the graph stretches and shifts.