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: $(2\pi - \theta)$
We can see that the angle $\dfrac{17\pi}{6}$ is close to $\dfrac{18\pi}{6}=3\pi $.
Thus, the reference angle of $\dfrac{17\pi}{6}$ is:
$ = 3\pi - \dfrac{17\pi}{6} $
$\implies =\dfrac{18\pi}{6} - \dfrac{17\pi}{6}$
$ =\dfrac{\pi}{6}$
