Answer
$\dfrac{\pi}{3}$
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 $\dfrac{13\pi}{3}$ is close to $\dfrac{12\pi}{3}=4\pi $.
Thus, the reference angle of $\dfrac{13\pi}{3}$ is:
Thus, the reference angle is:
$ = \dfrac{13 \pi}{ 3} -4\pi $
$\implies =\dfrac{13 \pi}{3} - \dfrac{12 \pi}{3}$
$ =\dfrac{\pi}{3}$
