Radians for Dummies

Measuring slope

As one of Mattel's more ill-conceived Barbie dolls, a talking model, once said, "Math class is tough!" It's apparent that mathematics is pretty much a black box for many of the Barbies of the literary world, those self-appointed freelancers who contribute to content farms on the internet. Take, for example, eHow.com's Chance E. Gartneer, already caught practicing his own rather strange version of arithmetic on another occasion. Today, we find Chance holding forth on a second topic with which he apparently has limited familiarity, in which he instructs his readers "How to Calculate Radians From a Slope" (now at Sciencing.com).

Chance immediately displays his ignorance of his topic in eHow's required "introduction" (75-100 words):

The radians of a slope refer to its angle measurement. Radians are angle measurement units that stem from pi, a mathematical constant that is commonly known as 3.14, but is in fact an infinite and patternless number. A slope, also known as a gradient, is the ratio between the growth or decrease in vertical and horizontal distances between two defined points. You can easily calculate a slope's angle measurement in radians through the simple inverse trigonometric arctangent or arctan function, which works in reverse to find the angle of a tangent value."

"The radians of a slope"? Pi is "commonly known as 3.14"? Slope is "the ratio between the growth or decrease in vertical and horizontal distances between two defined points"? All of those assertions (and more) suggest that Gartneer simply reworded a string of definitions without actually understanding them. Slopes don't "have" radians, they're measured in radians. Pi is an irrational, non-repeating decimal commonly expressed as 3.14 . Slope is the ratio of change in height to change in length.  Couldn't he just say those things? We guess not: the content editor would probably think he was plagiarizing. So now for the meat of the matter, Chance's "instructions": "Divide growth in the vertical distance by the growth in horizontal distance to find the degree of the gradient."  Actually, that's the slope; not the "degree of the gradient." "Calculate the arctan of the degree of the gradient to calculate the measure of its angle in radians on your scientific calculator." "Arctan"? Didn't you mean the "arc tangent," Chance? Or had you never heard of an arc tangent before... "Check your answer with an online arctan calculator." Duh.

We had to laugh, really: we can't tell whether Chance doesn't know what he's talking about or whether he does and is such a lousy writer he can't express it. We're leaning toward a 60:40 mix of the two. So if you really want to know the answer, here it is:

1. Divide change in Y by change in X to calculate the slope as a decimal number.
2. Take the arc tangent of the decimal slope to convert the slope to degrees (yes, you may use a calculator)
3. Multiply the slope in degrees by 0.0174533 to convert it to radians.

Why that last step? Because the number of radians in a circle is two times pi, and the number of degrees in a circle is 360. Thus, each radian corresponds to 360 divided by 2*pi degrees, or 57.29577 degrees per radian. One degree is the reciprocal of that number, or (approximately) 0.0174533 radians.

That way you know the slope in all three units. And it's easy, too! If you're pressed for time and have a scientific calculator (and can remember how to use it) you can always set the angle measurement to radians and skip step 2; though that's probably not necessary. However, if you follow these simple directions – by which we mean directions that haven't been padded to meet eHow's minimum word count – you are far less likely to be the Antisocial Network's Dumbass of the Day than "Chance E. Gartneer"!

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