Uses computer graphics to show how successive Taylor polynomials for sine x provide better and better approximations. Compares the range of accuracy for a family of Taylor polynomials and recaps the technique of evaluating function derivatives at x + 0 to determine the Taylor polynomials. Illustrates the use of a "function synthesizing machine" to determine the precise "mix" for any function. J. Richmond and J. Jaworski. From the Mathematics: A Foundation series.