1. The problem asks for the sine of the value $$-\frac{1}{2}\sqrt{7}$$. 2. First, recognize that $$\sqrt{7}$$ is approximately 2.64575, so $$-\frac{1}{2}\sqrt{7} \approx -\frac{1}{2} \times 2.64575 = -1.322875$$. 3. We want to find $$\sin\left(-1.322875\right)$$ where the angle is in radians. 4. Using the sine function property, $$\sin(-x) = -\sin(x)$$, so $$\sin(-1.322875) = -\sin(1.322875)$$. 5. Calculate $$\sin(1.322875)$$ using a calculator or approximation: $$\sin(1.322875) \approx 0.9689$$. 6. Therefore, $$\sin\left(-\frac{1}{2}\sqrt{7}\right) \approx -0.9689$$. Final answer: $$\sin\left(-\frac{1}{2}\sqrt{7}\right) \approx -0.9689$$.