Question

question find an angle \\( \theta \\) coterminal to \\( \frac{19\pi}{6} \\), where \\( 0 \leq \theta < 2\pi \\). answer attempt 1 out of 2 \\( \pi \\) submit answer

Explanation:

Step1: Subtract full rotations ($2\pi$)

To get an angle in $0 \leq \theta < 2\pi$, subtract $2\pi$ (or $\frac{12\pi}{6}$) from $\frac{19\pi}{6}$ until the result is in the interval.
$\frac{19\pi}{6} - \frac{12\pi}{6} = \frac{7\pi}{6}$

Step2: Check interval validity

$\frac{7\pi}{6}$ is between $0$ and $2\pi$ ($\frac{12\pi}{6}$), so it is valid.

Answer:

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