Constructing a Sine Curve by Dividing a Unit Circle into n Equal Parts

This applet demonstrates how to construct a sine curve by dividing a unit circle into n equal parts. By selecting n equally spaced points around the unit circle and using geometric projections based on the definition of trigonometric functions, the applet dynamically illustrates the step-by-step formation of the sine function graph. As the parameter n is adjusted, learners can observe how increasing the number of division points produces a progressively smoother and more accurate representation of the sine wave. The construction combines fundamental geometric objects such as circles, line segments, and sequences, providing a clear visual bridge between circular geometry and trigonometric graphs. This interactive approach reveals the intrinsic connection between the unit circle and trigonometric functions, showing how the vertical coordinates of points on the circle directly correspond to values of the sine function. The applet is designed for high school mathematics classrooms and self-directed exploration, making it an effective teaching and learning tool for trigonometry and function graphing. Students can manipulate the slider controlling n to explore the relationship between discrete point placement and continuous curve generation, deepening their conceptual understanding of periodic functions, amplitude, and the radian-based parameterization of the sine curve.