Question

Can somebody explain this definition? **The radian is the plane between two radii of a circle which cut off on the circumference an arc, equal in length to the radius**

Answer 1

I tried this:

Explanation:

I know ...it was steep for me too at first...
Consider the diagram:

we use the radian to indicate the "space" between the two red radii representing...an angle...the angle `alpha`!!!!

This is quite good because the requirement to have one radian is that the angle `alpha` is formed by the two red radii and the green arc that has itself the same length of the radius!!!
This is a good way to express the "measure" of an angle (the "space" between the two radii) because it has no dimension (quite useful in case of mixed operations) as in the case of degrees `"degree"°`.

The problem is that it is easier to "see" degrees and not so easy to "see" radians.

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A way to bridge between the two representations is to consider a circle of radius `r=1`;
consider the length of the entire circumference (a completely closed arc):

`C=2pir=2pi`

this is the length of the complete circumference and represents `2pi` radians BUT to produce the entire circumference we describe an angle of `360^@` so we get that:

`2pi` radians correspnds to `360^@`

Hope I didn't confuse you even more...