Q
QuestionMathematics

Explain why 2π radians equals 360 degrees.
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Answer

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Step 1
: Recall the definition of radian measure.

A radian is the measure of the central angle that intercepts an arc of length equal to the radius of the circle. In other words, if the arc length is equal to the radius, then the angle subtended by that arc at the center is 1 radian.

Step 2
: Understand the relationship between the circumference and the diameter of a circle.

The circumference C of a circle is given by the formula C = πd, where d is the diameter of the circle.

Final Answer

2π radians equals 360 degrees.