What Is 1 Radian | MATHVOX

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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.

Similar topics

Radians and Degrees. Measuring Angles in Trigonometry

Radian Measure of angles. Formula

Formula for converting degrees to radians. Formula for converting radians to degrees

Connection of the radian with other units (minutes and seconds)

A Unit Circle. Definition

Determining the Angle of Rotation, Radius Vector

Coterminal Angles

Reference Angle

Magnitudes of the rotation angles

The property of subsequent rotations

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Written and reviewed by the MathVox Editorial Team (All MathVox materials are created and edited to ensure clarity and accuracy in math education.)

Topics in Trigonometry

Geometry

Trigonometry

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