The lighthouse beacon: what mathematical questions can you ask?
Some questions
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.