a,
$\cos\dfrac{22\pi}{3}=\cos\dfrac{24\pi-2\pi}{3}=\cos\Big(8\pi-\dfrac{2\pi}{3}\Big)=\cos\dfrac{-2\pi}{3}=\cos\dfrac{2\pi}{3}=\cos\Big(\pi-\dfrac{\pi}{3}\Big)=-\cos\dfrac{\pi}{3}=-\dfrac{1}{2}$
b,
$\sin\dfrac{23\pi}{4}=\sin\dfrac{24\pi-\pi}{4}=\sin\Big(6\pi-\dfrac{\pi}{4}\Big)=\sin\dfrac{-\pi}{4}=-\sin\dfrac{\pi}{4}=-\dfrac{1}{\sqrt2}$