What is the coterminal angle of \(-\frac{41\pi}{9}\) between (0) and \(2\pi\)?

Correct answer: \(\frac{13\pi}{9}\)

To find a coterminal angle, add or subtract an integer multiple of \(2\pi\). \(-\frac{41\pi}{9}+3(2\pi)=-\frac{41\pi}{9}+\frac{54\pi}{9}=\frac{13\pi}{9}\). Since \(0<\frac{13\pi}{9}<2\pi=\frac{18\pi}{9}\), it lies in the required interval. Although \(\frac{11\pi}{9}\) is close, its difference from the given angle is not an integer multiple of \(2\pi\). Exam tip: use a common denominator to check that the final angle lies between \(0\) and \(2\pi\).