Respuesta :
pi radians in a semicircle (half circle)
2pi radians in a full circle.
2pi = 2*3.14 = 6.28 approximately, so there are approximately 6.28 radians in a full circle.
2pi radians is equivalent to 360 degrees.
The correct option is there are exactly π radians in a semicircle.
We know that the length of an arc in radians L = rθ where
- r = radius of the circle and
- θ = angle of sector.
For a semi-circle, l = πr
So, πr = rθ
θ = π
So, the angle subtented by the semi-circle is π radians.
Now for a full circle, l = circumference of the circle = 2πr.
So, 2πr = rθ
θ = 2π
So, the angle subtented by the circle is 2π radians.
So, the correct option is there are exactly π radians in a semicircle.
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