Let us consider a circle of radius r

 

Let Angle subtended by whole circle at center be θ

Length of arc = Circumference of circle = 2πr

 

Angle at center of circle in Radians.jpg

Now,

We know that

θ = l/r

θ = 2πr/r

θ = 2π

 

∴ Angle at center of circle in Radians is 2 π

  1. Chapter 3 Class 11 Trigonometric Functions
  2. Concept wise
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Let us consider a circle of radius r Let Angle subtended by whole circle at center be θ Length of arc = Circumference of circle = 2πr Now, We know that θ = l/r θ = 2πr/r θ = 2π ∴ Angle at center of circle in Radians is 2π

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