Because a transcendental function is not defined using a finite sequence of standard arithmetic operations, schemes other than arithmetic usually specify the evaluation of such functions. Recall that the usual definition of sine revolves about the construction of a unit circle centered at the origin of an xy-plane from which sine is produced by referencing a positive arc q of the circle traced counter-clockwise from the initial point (1,0) to a terminal point labeled (cos q, sin q).
If the student is able to follow the unit circle construction, the introduction of the graph of sine may confound their understanding. No longer is the unit circle embedded in an xy-coordinate system, so that certain x values represent the cos q and certain y values represent sin q where q is “wrapped” about the unit circle. Instead, q is mapped to the x-axis and cos q and sin q are both mapped to the y-axis in a new xy system.
On the other hand, a unit cylinder ties the unit circle directly to the graph of sine and also connects the graph to the identity function I(x) = x. The method of construction requires only some transparency medium, a straight edge, and a marker. You may use colored markers for more pizazz in the construction. For clarity, suggested marker colors are listed in the instructions. Use transparent tape to hold the structure together. As a result, without expensive equipment, an instructor, a student or small group of students will be able to construct the unit cylinder and experiment with its properties.
 | Preliminaries |
| Introduction |
| Construction |
| Discussion |
| Experiments |
| Conclusion |