How to change degree measure into radian measure: formula, proof, examples, and their solutions.
Radian is a way to write the measure of an angle
by the length of the unit circle's arc.
(Unit circle: r = 1)
To change the degree measure to radian measure:
(radian) = (π/180)⋅(degree).
The unit of radian measure is written as 'rad'.
But, mostly, it is omitted.
Recall the length of an arc formula:
l = 2πr⋅(θ/360)
The definition of radian measure
is the length of the unit circle's arc.
So l = (radian).
The unit circle's radius is 1.
So r = 1.
The arc formula's θ is in degree measure.
So θ = (degree).
Then (radian) = (π/180)⋅(degree).
To find the radian measure,
multiply (π/180) to the degree measure.
So 360º = 2π (rad).
Just like this,
you can write the other angles
in radian measure.