Answer: [tex]\bold{\dfrac{3\pi}{2}}[/tex]
Step-by-step explanation:
Coterminal means it is in the same place on the Unit Circle but one or more rotations clockwise or counterclockwise.
Note: one rotation is 2π (which is equivalent to [tex]\frac{4\pi}{2}[/tex])
[tex]-\dfrac{13\pi}{2}+\dfrac{4\pi}{2}=-\dfrac{9\pi}{2}\\\\.\qquad\qquad\quad=-\dfrac{9\pi}{2}+\dfrac{4\pi}{2}=-\dfrac{5\pi}{2}\\\\.\qquad\qquad\qquad\qquad\qquad\quad=-\dfrac{5\pi}{2}+\dfrac{4\pi}{2}=-\dfrac{\pi}{2}\\\\.\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad=-\dfrac{\pi}{2}+\dfrac{4\pi}{2}=\dfrac{3\pi}{2}\\\\\\\dfrac{3\pi}{2}\text{ is between 0 and }2\pi\text{ so this is the angle we are looking for!}[/tex]
