Sine and Cosine Function Graphs

In 3.3 we found that a pedal on a rotating crank has height $28 + 17 \sin \theta$. To understand motion like that, we need to see how $\sin \theta$ itself behaves as $\theta$ changes. In this note we turn the unit circle into two graphs, $y = \sin \theta$ and $y = \cos \theta$. Everything about these graphs — their shape, their range, and why they repeat — comes straight from a point moving around the circle.