Measuring Angles in Radians

What is a Radian?

A radian is an angle that subtends an arc whose length is equal to the radius of the circle.

It is abbreviated as "rad."

$$ 1 \ rad $$

Typically, if an angle is given as a single numeric value without any symbol, it is understood to be in radians.

Given that the circumference of a circle with radius r is 2πr, we can deduce that a full circle measures 2π radians.

Here, the symbol π, or pi, represents a constant approximately equal to $$ \pi = 3.14 $$.

Proof. To determine how many times the radius fits into the circumference, we divide the circumference (2πr) by the radius. $$ \frac{2 \pi r}{r} = 2 \pi \ rad $$ The result is two pi (2π) radians.

Therefore, we can express a full angle (360°) as 2 pi radians (2π).

Similarly, a straight angle (180°) is pi radians (π).

And so forth.