Why do radians even exist? Why would you use them instead of degrees?
In: Mathematics
Radians are basically the native angle measurement inherent in a circle that enable direct translation of angles to other aspects of geometry, and through this are the native angle measurement inherent in trigonometry where the math presents much more elegantly than using degrees, especially when you start to get into complex numbers and calculus.
For a basic example:
How long is the arc of a circle radius R drawn by an angle “A” – in Radians this is simply R times A. Similarly using radians the area of the sector enclosed by this angle is simply R^2 times A/2. If you measure the angle in degrees you have to do other gymnastics to get to the same place.
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