Taylor series help

Are you sure this is the right question. I don't see any way of doing this without doing some 40+ digit calculations, and I can't see that being expected.

yh that's all it says.

I have to give answer to 6dp

Well, you need to divide 10^42+1.2 by (2pi), getting an answer accurate to at least 7 decimal places (i.e. about 49 significant figures).

Take the fractional part of that answer. (e.g. (10^3 + 1.2) / (2pi) = 159.3459290 and you would reduce this to 0.3459290 ).

To get faster convergence, if this answer is bigger than 0.5, subtract 1.

Now multiply by 2pi (so here 0.3459290 becomes 2.1735360).

This new number has the same sin as the original.

You can now evaluate this using the normal Taylor series; you'll need to take about 8 terms to get 6 digits of final accuracy.

Again, you really don't want to do this without access to an extended precision calculator. I can't help feeling there's something missing here.

[Is there any chance you're supposed to be working with degrees rather than radians? It would make life a bit less painful].

It doesn't say whether degrees or radians; I assumed radians

Why do you divide by 2pi just once?

At first I thought I would just keep on dividing by 2pi to get a smaller value, then use the Taylor series.

The sequence of operations (multiply, take fractional part, multiply) is the same as reducing the argument modulo 2pi. You only need to do this once (the number doesn't change it you do it again) but you have to do the calculations to 50sig figs. There's no way round this and it's the biggest problem here.