6) sin((3π/2)-(4π/3))

Explanation:

Step1: Calculate the value inside the sine - function

First, find a common denominator for the fractions inside the parentheses. The common denominator of 2 and 3 is 6. So, (\frac{3\pi}{2}-\frac{4\pi}{3}=\frac{3\pi\times3}{2\times3}-\frac{4\pi\times2}{3\times2}=\frac{9\pi}{6}-\frac{8\pi}{6}=\frac{9\pi - 8\pi}{6}=\frac{\pi}{6}).

Step2: Evaluate the sine - function

We know that (\sin(\frac{\pi}{6})=\frac{1}{2}).

Answer:

(\frac{1}{2})