What Is a Radian... for Dummies

radian definition

The staffer who specializes in mathematics has had a rough couple of months, what with a head cold that just wouldn't let go and then, of all things, a ruptured eardrum. It was weird watching blood run out of the poor kid's ear! But he's back, and we thought we'd let him ease into action with something he says is almost a gimme. Let's have a look, then at what he turned up: repeat DotD John Papiewski (sometimes known as J. T. Barett) and the Sciencing.com post, "What Is a Radian?"

As we sometimes do, we'll set the record straight up front before going through Papiewski/Barett's attempt to define the term "radian." Simply put, radians are an alternate measure of angles that are distinct from degrees. The precise definition of one radian is the angle subtended by an arc of a circle whose length is equal to the radius. A little thought, then, will suggest that a circle comprises 2 π radians, because the circumference of a circle is 2 π times the radius. It's not that hard...

Well, maybe for Papiewski. Here's what he thinks is the definition of a radian:

"The segment of a circle’s circumference that corresponds to the angle made by two radius lines makes an arc. The angle that this arc creates, when you draw lines from its starting and end points to the circle’s center, is one radian."

See what's missing? Right: John says nothing whatsoever about the length of the arc, which is critical to the definition of he measurement. In fact, the "angle made by two radius lines" could be any angle between 0 and 360 degrees.

Not content to leave it there – and required by the site to publish at least 300 words in his "answer" – Papiewski went on to botch more facts. Well, if you know how to interpret what he said, he's sort of right. Sloppy, but correct:

"A circle, for example, has 360 degrees, a triangle has 180 and a right angle has 90."

Not how our math whiz would word it, but close enough for eHow.com. Still short of words, though, Papiewski decided to pad his text with something that would 1) flummox a "content editor" with a "creative writing' or "communications" degree and 2) make him look smart. That's where this bit of rubbish came from:

"In degrees, the function looks like this:   sin(x) = (π × x ÷ 180) - (π × x ÷ 180)3 ÷ 3! + (π × x ÷ 180)5 ÷ 5! - (π × x ÷ 180)7 ÷ 7! + (π × x ÷ 180)9 ÷ 9! ... For this power series, note that you need to repeat the “π × x ÷ 180” for every term – a lot of extra writing and calculation compared to the neater, more compact equivalent in radians."

Again, mathematically correct... but what a waste of space! Especially since our Dumbass of the Day had already blown the definition in the first paragraph...

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