Answer
$-1$
Work Step by Step
We need to compute $\sin(\dfrac{11\pi}{2})$
The trigonometric function $\sin$ has a period of $2\pi$. So, we will find a value where the argument is between $0$ and $2 \pi$ in terms of the special angles.
Therefore,
$\sin(\dfrac{11\pi}{2})=\sin (\dfrac{(3+8)\pi}{2})\\ =\sin(\dfrac{3\pi}{2}+4\pi)\\=\sin(\dfrac{3\pi}{2})\\=-1$
