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a)
\sin\ \frac{\pi}{4}=\frac{\sqrt{2}}{2}
b)
\cos\ \frac{7\pi}{6}=\frac{-\sqrt{3}}{2}
c) 
\sin\ \frac{8\pi}{3}=\sin\ \frac{2\pi}{3}=\frac{\sqrt{3}}{2}
d)
\cos\ \frac{9\pi}{4}=\cos\ \frac{\pi}{4}=\frac{\sqrt{2}}{2}
e)
\sin\left(-\frac{\pi}{3}\right)=\sin\ \frac{5\pi}{3}=\frac{-\sqrt{3}}{2}
f)
\cos\left(-\frac{\pi}{6}\right)=\cos\ \frac{11\pi}{6}=\frac{\sqrt{3}}{2}