Why do radians even exist? Why would you use them instead of degrees?
In: Mathematics
Radians are really useful when you need to convert from a rotating context to a straight line (linear) context, and vice versa.
For example, if you have a wheel with a radius of 1 meter, this means that each time the wheel rotates 1 radian, it also travels forward 1 meter. So if the wheel rotates at 1,000 radians per hour, we immediately know that we are also moving forward at 1,000 meters per hour; also known as 1 kilometer per hour.
This context switching between rotating and linear contexts happens *a lot* in engineering, so it’s really convenient to have a unit of measure that expresses angles in a way that we can very easily convert to linear measurement.s
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