Answer
$\dfrac{\pi}{6}$
Work Step by Step
The reference angle of an angle $0 \leq \theta \lt 2\pi $ based on its position can be computed by using the following steps:
a) Quadrant- I: $\theta $
b) Quadrant -II: $(\pi-\theta)$
c) Quadrant- III: $(\theta - \pi)$
d) Quadrant - IV: $(2\pi - \theta)$
First we subtract $360^{\circ}=2\pi$:
$\dfrac{17\pi}{6}-2\pi=\dfrac{5\pi}{6}$
We are in quadrant 2, so subtract from $\pi$:
$\pi-\dfrac{5\pi}{6}=\dfrac{\pi}{6}$
