Trigonometry Types for Dummies

triangle types

The newest intern at Antisocial Network HQ thought she'd recognized a pattern: freelancers with liberal arts backgrounds demonstrating their ignorance of the so-called STEM subjects. We thanked her for her effort, even though everyone here already knew that most of the contributors to the former Demand Media Studios were journalism graduates who'd studiously avoided the sciences... well, not all of them: Brooke Ashley has a "creative writing" BA, but she's still mathematically illiterate. She proved that with her post, "Types of Trigonometry," at Sciencing.com...

According to Ashley, there are four types of Trig: core, plane, spherical, and analytic. Our problem is that we can't find anywhere other than this article that cites four types of trigonometry, and we're loath to take the word of a creative writing major about math. After all, Brooke is the one whose introduction claims that

"Trigonometry is a branch of mathematics that uses variables to determine heights and distances..."

...which we thought was a rather strange way to describe the branch of mathematics that is most concerned with angles! Heck, that sounds more like algebra than trig, anyway. But let's see how she differentiates among those four types. These are her... definitions:

Core: "This type of trigonometry is used for triangles that have one 90 degree angle." The obvious point here is that it's impossible for a triangle to have more than one 90-degree angle. And why doesn't she call it a "right triangle" like everyone else in the world? "Mathematicians use sine and cosine variables within a formula (as well as data from trigonometry tables such as decimal values) to determine the height and distance of the other two angles." What is this hang-up with "height and distance," anyway? Why can't she use the word "length"? Plane: "Plane trigonometry is used for determining the height and distances of the angles in a plane triangle. This type of triangle has three vertices (points of intersection) on the surface, and the sides of the triangle are straight lines. Values for plane trigonometry are different than for core, as the sum of the plane must equal 180 degrees as opposed to 90 degrees." Dear Lord, where on Earth did this woman get the idea that there are triangles whose "sum of the plane" isn't 180 degrees??? And how does this differ from "core," anyway?

Spherical: "Spherical trigonometry deals with triangles that are drawn on a sphere... Unlike core or plane trigonometry, the sum of all angles in a triangle is greater than 180 degrees." Brooke clearly has no idea whatsoever how those angles are defined and why they sum to more than 180 degrees. We're not even sure she knows how many angles there are... HINT: three. Analytic: "The sine (and cosine) of the sum of two angles is used to obtain the sine (and cosine) of a double angle. Formulas for double angles are also used to determine the values of half angles, by using division and square roots. Analytic trigonometry is used in engineering and science." Brooke cunningly just plucked some words from this page and decided it was a different kind of trig. It's not; it's just drilling deeper into trigonometry... but what's this "x-y plane of a triangle" crap anyway, Brooke?

By the time she gets to the last line of her post, Ashley is hip-deep in bull-puckey. That's understandable, considering that she probably hadn't taken a math course since her sophomore year in high school, and may have never taken trigonometry at all! Heck, the woman probably thinks the Pythagorean theorem is some kind of flaming Jello shot, which is all we need to know to crown her Dumbass of the Day.

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