Answer
$\dfrac{\pi}{4}$
Work Step by Step
$\dfrac{11\pi}{4}$ is close to $\dfrac{12\pi}{4}=3\pi$.
This means that this angle is between $2.5\pi$ and $3\pi$.
RECALL:
An angle $\theta$, where $2.5\pi \lt \theta \lt 3\pi$, is coterminal with:
$\theta - 2\pi$
Thus, the given angle is coterminal with:
$=\dfrac{11\pi}{4} - 2\pi=\dfrac{11\pi}{4} - \dfrac{8\pi}{4} = \dfrac{3\pi}{4}$
$\dfrac{11\pi}{4}$ is coterminal with $\dfrac{3\pi}{4}$.
$\dfrac{3\pi}{4}$ is in Quadrant II so $\dfrac{11\pi}{4}$ is also in Quadrant II.
RECALL:
The following are the means on how to find the reference angle of an angle $0 \leq \theta \lt 2\pi$ based on its position:
(1) Quadrant I: $\theta$ (itself)
(2) Quadrant II: $\pi-\theta$
(3) Quadrant III: $\theta - \pi$
(4) Quadrant IV: $2\pi - \theta$
Use formula (2) above to obtain:
reference angle of $\dfrac{11\pi}{4}$ = reference angle of $\dfrac{3\pi}{4}$, which is
$\\=\pi - \dfrac{3\pi}{4}
\\=\dfrac{4\pi}{4} - \dfrac{3\pi}{4}
\\=\dfrac{\pi}{4}$
