Why do radians even exist? Why would you use them instead of degrees?
In: Mathematics
For small angles, say less than 5°, the angle in radians is equal to the sine. So there’s no need to convert to degrees. You just take a ratio and you’re done.
Let’s say something is 100 m away and has a height of 5 m. That means it occupies 5/100, or 0.05 radians (50 milliradians, or 50 mrad) of your field of view. To convert to degrees you have to divide by pi and multiply by 180, because 180° is equal to pi radians. That makes the angle 2.86°.
Why go through the extra step of converting to degrees when using units of radians is just as valid? For quick reference, I’ve memorized that 57° is 1 radian, and 1° is ~17 mrad. Because I’m fun like that.
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