Question

find a positive angle less than 2π that is coterminal with the given angle.
\\(\frac{19pi}{6}\\)
a positive angle less than 2π that is coterminal with \\(\frac{19pi}{6}\\) is \\(square\\).
(simplify your answer. type your answer in terms of π. use integers or fractions for any numbers in the expression.)

Explanation:

Step1: Identify coterminal angle rule

Coterminal angles differ by $2\pi$ multiples.

Step2: Subtract $2\pi$ (convert to sixths)

$2\pi = \frac{12\pi}{6}$, so $\frac{19\pi}{6} - \frac{12\pi}{6} = \frac{7\pi}{6}$

Step3: Check angle range

$\frac{7\pi}{6}$ is positive and less than $2\pi$ ($\frac{12\pi}{6}$).

Answer:

$\frac{7\pi}{6}$