What is the coterminal angle of \(-\frac{23\pi}{6}\) between (0) and \(2\pi\)?

Correct answer: \(\frac{\pi}{6}\)

The direct answer is A, \\(\frac{\pi}{6}\\). Coterminal radian angles differ by multiples of \\(2\pi\\). Start with \\(-\frac{23\pi}{6}\\). Since \\(2\pi=\frac{12\pi}{6}\\), add suitable full turns until the result lies between 0 and \\(2\pi\\): \\(-\frac{23\pi}{6}+\frac{24\pi}{6}=\frac{\pi}{6}\\), which is in the required interval. Option A is correct. Option B, \\(\frac{\pi}{3}\\), differs from the original by a non-integer number of full turns. Option C, \\(\frac{5\pi}{6}\\), is likewise not coterminal. Option D, \\(\frac{11\pi}{6}\\), is positive and in the interval, but it is not obtained by adding an integer multiple of \\(2\pi\\) to the given angle. The supplied calculation using \\(4\pi\\) is exactly the same: \\(-\frac{23\pi}{6}+4\pi=\frac{\pi}{6}\\). Memory cue: in radians, add or subtract \\(2\pi\\), not \\(360\\).