Why do radians even exist? Why would you use them instead of degrees?
In: Mathematics
The weird thing about both radians and degrees is that they are both extremely useful in their appropriate applications. As a species, we so rarely do this well, but the usefulness of radians to any associated math or science, and degrees to ease of communication and divisibility is the rare time we got them both kind of right. Think about this for a second, we could have had gradians instead of degrees. Can you imagine what kind of a nightmare that would have been? 400 gradians in a circle. Divisible by so few numbers compared to 360.
I’ve been on both sides of this. When I was a pilot full-time, degrees were extremely natural and easy to use. Now, as a software engineer that does a lot of lat/long and heading/course manipulation, I use radians and degrees almost interchangeably. Degrees are good for course and heading selection. When those values have to be mathed into vectors for calculations, trig functions are called, which almost always take radians. Still, I always prefer to think in degrees. Some aspects of flying never leave you.
Some people will tell you radians are not a unit. Do not listen to them. They are a unit of measurement. Dimensionless, sure, but still a unit. I can measure turn speed in radians per second, definitely a unit of measurement. Somehow “I was turning at 0.2, uh, <blank> per second” doesn’t work.
One more nugget:
In some dark corners of industry, there is such a thing as a Pi-Radian. Take a normal radians value and divide by PI. Circles are 2 Pi-Radians. Not 2 Pi, just 2. It makes some math easier. Now, I’m not saying anyone should use Pi-Radians, only that they would still be better than Gradians.
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