Answer
a) $\dfrac{4 \pi}{3}$
b ) $\dfrac{\pi}{3}$
Work Step by Step
The co-terminal and 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: $(2\pi - \theta)$
a) The positive angle is less than $2 \pi $; this means the co-terminal with $\dfrac{16 \pi}{3}$ is $\dfrac{16\pi}{6} -4 \pi =\dfrac{4 \pi}{3}$
b ) Thus, the reference angle of $\dfrac{16 \pi}{3}$ or, $960^{\circ}$ is $\dfrac{\pi}{3}$ or, $60^{\circ}$
