I have written a Mathematica notebook that uses Taylor series to compute the sine function. At the 2007 Kansas City Regional Math Technology Expo, I gave a talk on my sine calculator and outlined a possible Calculus II project to have students write such a calculator.
There are two versions of the sine calculator. For the professional version, the user inputs the sine value to be computed and an epsilon, which determines the desired accuracy. The output is minimal. The teacher's version lets the user choose the number of decimals to display and gives more output in order to illustrate the underlying mathematics. I would be happy to send you a copy of the Mathematica notebooks if you like.
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