a) Determine an exper value for the sppression sin(5pi )/(4)=cos(11pi )/(6)cot(pi )/(3)

## Step1: Evaluate $\sin \frac{5\pi}{4}$<br />### The angle $\frac{5\pi}{4}$ is in the third quadrant where sine is negative. The reference angle is $\frac{\pi}{4}$. Therefore, $\sin \frac{5\pi}{4} = -\sin \frac{\pi}{4} = -\frac{\sqrt{2}}{2}$.<br />## Step2: Evaluate $\cos \frac{11\pi}{6}$<br />### The angle $\frac{11\pi}{6}$ is in the fourth quadrant where cosine is positive. The reference angle is $\frac{\pi}{6}$. Therefore, $\cos \frac{11\pi}{6} = \cos \frac{\pi}{6} = \frac{\sqrt{3}}{2}$.<br />## Step3: Evaluate $\cot \frac{\pi}{3}$<br />### The cotangent of an angle is the reciprocal of the tangent. $\tan \frac{\pi}{3} = \sqrt{3}$, so $\cot \frac{\pi}{3} = \frac{1}{\sqrt{3}} = \frac{\sqrt{3}}{3}$.<br />## Step4: Combine the results<br />### Substitute the evaluated values into the original expression: $-\frac{\sqrt{2}}{2} = \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{3}$. Simplify the right-hand side: $\frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{3} = \frac{3}{6} = \frac{1}{2}$.