I am going to learn trigonometry next year. I am an advanced student and I like to get a head start on things. So,
How do you describe and introduce Trigonometry to the advanced secondary school student who has had Algebra and Geometry?
A supplemental question is
What are the best texts or websites to introduce the subject to a curious or independent learner?
On
Literally, the study of triangles. Since a triangle may either be specified by its edge lengths or by its angles (up to scaling), in practice this means that trigonometry studies the relationship between angles and side lengths. Traditionally, the focus is on right triangles, which represent the majority of the challenge (any triangle can be cut into two right triangles).
Since there are triangles everywhere, trigonometry has many implications, for example in the motion of planets, springs, pendula, and waves.
On
Trigonometry is the study of triangles.
http://en.wikipedia.org/wiki/Trigonometry
It has vast applications in the real world and in theoretical maths. Wikipedia actually is one of the better starting points for learning about it. The introduction from Wolfram is more straightforward and less helpful for a newcomer:
http://mathworld.wolfram.com/Trigonometry.html
If you really want to start studying on your own, the Kahn Academy is a great place to listen to lectures:
https://www.khanacademy.org/math/trigonometry
Personally I found this book fascinating, it provides wonderful context for the basic subject, and you may continue to amaze (and annoy) your teachers by quoting from it. The reading could be difficult (or boring) for you, I would look for one in the library before buying it. But when you have to write a history paper, perhaps you can use this as a reference to write about mathematics if you find this subject more interesting!
http://www.amazon.com/The-Mathematics-Heavens-Earth-Trigonometry/dp/0691129738
The thing with the angles and the three-letter functions... Unless you meant it philosophically, as in What is art ?, and whatever...