How can I get a Taylor expansion of the Sin[x] function?

Question

How can I get a Taylor expansion of the Sin[x] function by the power series?

Answer 1

If you're new to Mathematica, then it might make sense to explore these kinds of basic things via the natural language interface. Assuming that you're connected to the internet, so Mathematica can access WolframAlpha's servers, just type

= power series sinx

Note that the equals sign will be reformatted to look like it's part of the WolframAlpha input window. The input and output taken together should look like so:

In addition to generating the series, this also shows you the precise Mathematica syntax to get the series - useful for when you graduate to higher level Mathematica usage!

It can be quite good at guessing your intent. In this particular case, we can type in the exact title of your question and get the correct result!