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Towards Maclaurin

Build series for the sine and cosine functions by adding one term at a time, alternately making the approximation too big then too small but getting ever closer.

Building Approximations for Sin(x)

Build up the concept of the Taylor series

Taking Trigonometry Series-ly

Look at the advanced way of viewing sin and cos through their power series.

What Do Functions Do for Tiny X?

Age 16 to 18 Challenge Level:

This problem begins to motivate the existence of the Maclaurin's series in which any function which is well-behaved at the origin can be written as an 'infinite polynomial' or 'power series'. This iterative method is a numerical way of finding the coefficients of the polynomial, although calculus can be used in cases where the derivatives of the function needing to be approximated are known.