Unit Circle

Recently I was asked to include a copy of the Trigonometry Unit Circle in a Year 10 Extension Maths exam. When I went looking for a good one on the Internet, I found plenty of Unit circles that were good for concept teaching, but weren't very detailed. Some had no angle labels at all.

We also had one that had been hand drawn and scanned, but it wasn't very accurate or neat. That unfortunately was the one I used, as the exam timetable was approaching fast.

So once I had some free time, I scratched one together using SageMath.

MathJax for the win.

Just a little note that I use MathJax for my mathematical posts, and this is the ONLY scripting (so far) that I throw into my blog.

Here are some of the resources I use for MathJax:
http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference
http://www.suluclac.com/Wiki+MathJax+Syntax

and here's how I add it:
http://mathjaxtest.blogspot.com.au/
The one thing missing in this post, however, is that you need to close the </script> tag. :/

Why does e = 2.71828183? Or how e SHOULD have been discovered.

This is an interesting exercise to do with higher level mathematical students - it shows them that the value of $e$ can be derived purely from it's differential properties.

So we start with the fundamental property of $e$, that $D(e^x)_x = e^x$.
In short, we're looking for the identity function of differentiation - what function stays unchanged.
(As noted in previous posts, I'm using a differential format similar to sagemath's default format.)