Friday, April 6, 2007

Trig? Oh NO! Metry.

Let's learn some Math today.

You’re thinking: Boooo! Math blows! Show me your tits!

I’ll admit that most of Math is tedious and frustrating, but some subjects within the realm of Math can actually be useful. Like Trigonometry.

I didn’t appreciate Trigonometry when I was learning it, but looking back on it now I have very fond memories of my days in Trig class. My friendship with Sine and Cosine and Tangent has stood…uuuhh, standed? withstood (?) the test of time. I remember this one time that Cosine got so black-out drunk and threw up in my car! I’ll warn you, folks, do NOT give that function Tequila. Good times.

This might be a stroll down memory lane for some of you, and for others it may seem like I’m taking you down a poorly lit back ally where you are going to get stabbed for your shoes. Don’t worry. If anyone stabs you and steals your shoes it’s going to be me. You have nothing to fear from Math. In fact, Math might help you in this situation because god knows I’ll turn on you at the drop of a hat.

We’ll begin by looking at our friend, the triangle. A right triangle always has one 90º angle and two acute angles (angles less than 90º). Right triangles are where we get all of our Trigonometric constituents from, like sine, cosine, and tangent. Other types of triangles are:

Equilateral: all angles equal 60 º, all sides the same length
Isosceles: two sides are the same length, 2 angles are equal
Obtuse: one angle is bigger than 90º
Acute: all angles are smaller than 90º

Back to the right triangle. So we’ve got one angle of 90º (indicated by that boxy thingy in the corner) and two others that are less than 90º. Let’s define one of those angles as theta (the “O” looking thing with the line through the middle). Let’s also give each side a name: Stalin, Churchill, and Roosevelt. You get to brush up on your history today too! sin θ = opposite / hypotenuse = Churchill / Roosevelt
cosin θ = adjacent / hypotenuse = Stalin / Roosevelt
tangent θ = sin θ / cosin θ = opposite / adjacent = Churchill / Stalin

If we take these functions and flip around what’s on top (the numerator) and what’s on bottom (the denominator) we can define 3 more functions: secant, cosecant and cotangent

secant θ = upside-down cosine = hypotenuse / adjacent = Roosevelt / Stalin
cosecant θ = upside-down sine = Roosevelt / Churchill
cotangent θ = upside-down tangent = Stalin / Roosevelt

From here, Trigonometry takes the ball and runs with it. You get into identities, Pythagorean theorems, Reduction Formulas, Double-Angle Formulas, Power-Reducing Formulas, and so much more. It’s hard to appreciate that such a vast subject can be built on such simple principles. Drink it in folks, it's a profound concept. Trigonometry is my friend, and it can be your friend too!

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