Sine vs. Cosine vs. Tangent: get your trig on
Did you enjoy Newton vs. Leibniz, our last mathematical battle? Are you ready to get even mathier?
… Yes?
Yes.
Some of you may have gotten to trigonometry in your schooling. If you haven’t… well, trigonometry is mostly the study of triangles. A big fancy word for a surprisingly simple thing. Now check out this triangle.
That corner with the little square in it means we have a right triangle, which is a triangle with one angle of 90 degrees. The square corner is the 90 degree angle. We’re interested here in what we can do with the other two angles. Let’s pick angle α. There are a few numbers we can get from angle α…
The sine of angle α is a number derived from two measurements, firstly the length of the side opposite angle α, secondly the length of the hypotenuse (the triangle’s longest side). You express the sine as a ratio:
Next…
The cosine of angle α also uses the measurement of the triangle’s hypotenuse, but instead of using the length of angle α’s opposite side, we use the length of angle α’s adjacent side. So the cosine ratio looks like this:
Last (for now)…
The tangent of angle α cuts the hypotenuse out completely. To calculate the tangent, you just use α’s opposite side and adjacent side together, like so:
And those are the first three basic trigonometric functions!
*crickets*
Okay, okay. “So what?” Here’s the so what: mathematicians and scientists use these functions to help them model all kinds of things, from wave forms to the motion of celestial bodies. Musicians, astronomers, engineers, oceanographers, statisticians, and many more people can all thank the humble triangle and the humble trig nerds who figure this stuff out.
With that, lesson over. Here’s the competition. Which trig function suits your personality? Are you the contrarian sine, the neighborly cosine, or do your own mental tangents make you the world’s wild card? Pick your team, and starting at 11:00 AM EST on 1/14 you’ll have 24 hours to show off your proportions!
The usual bonuses
Earn 5,000 points – 2,500 bonus
Earn 15,000 points – 5,000 bonus
Earn 25,000 points – 10,000 bonus
For every 25,000 points above 25,000 – 5,000 bonus
Member of winning team (if you’ve scored at least 2,500 points) – 10,000 bonus
Highest scorer on each team – 5,000 bonus
Player with #1 overall score – 10,000 bonus
Player with #2 overall score – 5,000 bonus
Player with #3 overall score – 2,500 bonus