This activity combines the ideas of unit circle, and a line tangent to the unit circle to explain how Tangent (the trig. ratio) is related to the concept of tangent to a figure (from geometry). The intent is to briefly explore the mathematical history of the trigonometric ratio "tangent" through an interactive data-gathering construction, simulating an experience that may well mirror how values of trigonometric functions may once have been approximated.
Before the Activity
Download the attached .pdf or .doc file and read through the activity.
Note that students should have studied the three primary trigonometric ratios in a right triangle setting and have an understanding of similar triangles.
During the Activity
The activity is inter-active and exploratory in nature and well-suited for students working in pairs. Students should have a scientific calculator (or trig. tables) to serve as an independent verification of values they generate with the TI-Nspire.