### 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 18Challenge 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.