Answer
$\dfrac{ 3\pi}{8}$
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 are in quadrant 2, so subtract the given angle from $\pi$:
Thus, the reference angle is $\dfrac{8 \pi}{8}- \dfrac{5 \pi}{8}=\dfrac{ 3\pi}{8}$
