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.

 

 
 

Please feel free to point out any errors or typos, or share suggestions to improve these notes. English isn't my first language, so if you notice any mistakes, let me know, and I'll be sure to fix them.

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Angles (Geometry)