Maclaurin series

problem
Favourite

Taking Trigonometry Series-Ly

Age

16 to 18

Challenge level

2 out of 3

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

Building Approximations for Sin(x)

Age

16 to 18

Challenge level

3 out of 3

Build up the concept of the Taylor series
problem

Bessel's Equation

Age

16 to 18

Challenge level

3 out of 3

Get further into power series using the fascinating Bessel's equation.
problem

Trig Reps

Age

16 to 18

Challenge level

1 out of 3

Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?
problem

What Do Functions Do for Tiny X?

Age

16 to 18

Challenge level

2 out of 3

Looking at small values of functions. Motivating the existence of the Maclaurin expansion.
problem

Towards Maclaurin

Age

16 to 18

Challenge level

3 out of 3

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.