Why calculus?

Calculus Level 3

For a unit circle centered at \( (0,0) \), we draw \(n\) equally spaced chords parallel to the \(y\)-axis between \(x = -1\) and \(x = 1\). What is the limit of the average length of these chords as we let \(n\) tend to infinity?

Details and assumptions:

  • Any argument of a trigonometric function in the answer choices is in radians.
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