Want to explore the unit circle and the sine function graph? This interactive illustration shows how the sine graph forms as the angle changes. To interact with the tool below, drag the black point at the bottom left or right. Click “Record trace” to record the trace of the purple point. Click “Stop recording” to stop the trace. Click “Clear” to erase all recorded traces.
While exploring the interactive tool, use these points as a learning guide:
- What do the lengths of the green and purple lines on the x– and y-axes represent? How do they relate to the unit circle on the left?
- What does the purple point on the coordinate plane represent? When you move the slider left or right, how does the purple point move? What affects its movement?
- Click “Record trace” (if you haven’t yet), then move the slider left and right. What do the traces show? What would happen if all possible traces of the purple point were drawn?
Have fun exploring!