Answer
$\dfrac{\sqrt{2}}{2}$
Work Step by Step
$\sin{(\theta+2 \pi k}) = \sin{\theta}$
$\therefore \sin{\dfrac{9 \pi}{4}}=\sin{\left(\dfrac{\pi}{4}+ 2 \pi \right)} = \sin{\left(\dfrac{\pi}{4} \right)}$
$\sin{\left(\dfrac{\pi}{4} \right)} = \boxed{\dfrac{\sqrt{2}}{2}}$
