The lighthouse beacon: what mathematical questions can you ask?
- Given the angle of rotation of the lighthouse, what is the position of the spot of light on the shoreline?
- Given the position of the spot of light on the shoreline, what is the angle of rotation of the lighthouse?
- Can you graph the position of the spot as a function of this angle?
- Where do asymptotes occur on this graph? What is their meaning in context?
- Consider the directed distance of the light ray from the lighthouse to the spot on shore (use negative values for the “red” ray). Sketch a graph of this distance as a function of angle of rotation.