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A derivative per radian is how many times its per-degree value?

  • A.About 3
  • B.About 180
  • C.About 57
  • D.About 6

Answer: C

One radian is 57.3 degrees, so the per-radian value is that many times the per-degree one: a slope of 0.1 per degree is 5.73 per radian. Six is roughly \( 2\pi \), which is the numerical value of a thin-aerofoil slope per radian and easy to confuse with a conversion factor. Three is about half of that. One hundred and eighty is the number of degrees in \( \pi \) radians, not in one radian, and using it introduces a factor of \( \pi \) error.

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