Trig

The election is getting closer! Everyone has seen close-up coverage of the candidates, their VP, and their families.

So the name of Sarah Palin's youngest son is Trig. More people from the English-speaking world are now choosing their own names instead of pulling names from non-villian characters from the Bible.

Interesting name. It reminds me of the long forgotten subject of most people: trigonometry. Not sure if the Palins are thinking the same.

Although "trigonometry" is a long and formidable name, it is such fundamental subject: the study of triangles, right triangles in particular.

2 points determine a line; 3 points determine a triangle (and a plane). It is so fundamental. If you have 4 points you don't know for sure what you get.

In trig, students get introduced to functions, such as sin, cos, tan. They are more interesting than linear or polynomials they encounter in their high school algebra.

The side lengths of right triangles are dictated the Pythagorean theorem. The functions sin, cos, and tan have so many interesting relationships. If you spilled your favorite drink on your calculator and destroyed your cos and tan buttons you can still figure it out.

cos θ = sin (90° - θ) and of course, cos θ =sqrt(1-sin²θ)
tan θ = sin θ / cos θ (so you can figure out tan using sin)

That is just some very basic identities. I don't know why θ is so popular in naming angles. Please, please, Chinese/Hong Kong foreign students, don't pronounce it as thee-da.

What I think is way cool is that the derivative of sin is cos, and it is not super obvious how to derive this.

Sine/cosine can also be represented by a series:

sin x = x - x³/3! + x⁵/5! - x⁷/7!...

cos x = 1 - x²/2! + x⁴/4! - x⁶/6!...

That is Taylor series derived from calculus: alternate signs, odd powered, divided by odd factorials for sine, even powers and factorials for cosine... interesting isn't it?