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What are radians?

What are radians? Here are some definitions.

Noun
  1. plural of radian
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Examples
Another unique product offered by Radians is bifocal eye protection.
Given that the field oscillates at 60Hz, this gives me a phase angle of 0.4PI radians between samples.
Notice that the formula involves the use of the exponential function, and that the angles must be in radians.
The maximum deviation of the cantilever from horizontal was 0.06 radians, and so no mathematical or mechanical correction for rotation of the cantilever was implemented.
The sliding displacement between doublets may be found by multiplying the shear angle, in radians, by the interdoublet distance.
I can't tell the difference between radians, tangents, cotangents, secants, etc.

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