The values of 1 radian in degrees

 

1 radian

Or:

1 radian

1 radian

1 radian in degrees

Derivation of the value of 1 radian

 

When terminal side OM completes a full circle, point M goes along its entire circumference.

By definition, the circumference equals:

1 радиан

We substitute this value in the formula for determining the value of the angle: α = l/R:

1 радиан

In turn, the value of round angle α equals 360° (α = 360°). Therefore, since:

1 радиан

then:

1 радиан

therefore:

1 радиан

So, π rad equals 180 degrees:

π rad = 180°

therefore:

  • 1 rad equals 180 degrees divided by π;
  • 1 rad = 180°/π ;
  • 1 rad ≈57.295779513°, which is about one sixth of the circle.