Ever wondered why we go through all that trouble to convert degrees or radians and vice versa? And what exactly does it mean when we say 1 radian and how did we get there?
Well, a Radian, simply put, is a unit of measure for angles that is based on the radius of a circle. What this means is that if we imagine taking the length of the radius and wrapping it around a circle, the angle that is formed at the centre of the circle by this arc is equal to 1 Radian.
Now most of us are used to using the conversion formula for degrees to radians and vice versa but ever wondered how it came about? It's actually fairly simple. The circumference of a circle is 2 times π times r which means that there are approximately 6.28 Radians in a full circle.
Another way of thinking about this is to imagine you are standing in a circular park and you go for a walk around the outside of the park. You can either calculate this as walking the circumference of the park (which is 6.28 Radians) or walking 360 Degrees around it which in a way is the exact same thing
It is from this relationship that we say 2*π*r = 360 Degrees or that 1 Radian = 180/π Degrees and 1 Degree = π/180 Radians.