Answer
$-2$
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: $(2\pi - \theta)$
Thus, the reference angle of $\dfrac{ 22 \pi}{3}-\dfrac{21\pi}{3}=\dfrac{ \pi}{3}$
So, $ \sec \dfrac{ \pi}{3}=\dfrac{1}{\cos \dfrac{ \pi}{3}}=2$
Thus, we have $ \sec \dfrac{\pi}{3}= -2$ because $\theta $ lies in Quadrant-III.
