problem Trig reps Age 16 to 18 Challenge level Can you deduce the familiar properties of the sine and cosine functions starting from these three different mathematical representations?
problem Bessel's equation Age 16 to 18 Challenge level Get further into power series using the fascinating Bessel's equation.
problem Favourite Taking trigonometry series-ly Age 16 to 18 Challenge level 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 Build up the concept of the Taylor series
problem What do functions do for tiny x? Age 16 to 18 Challenge level Looking at small values of functions. Motivating the existence of the Taylor expansion.
problem Towards Maclaurin Age 16 to 18 Challenge level 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.