1. The problem asks for the value of $\sec\left(\frac{\sqrt{3}}{2}\right)$.\n\n2. Recall that $\sec(x) = \frac{1}{\cos(x)}$. So, we need to find $\cos\left(\frac{\sqrt{3}}{2}\right)$ first.\n\n3. Note that $\frac{\sqrt{3}}{2}$ is a number, not a standard angle in radians or degrees. Usually, trigonometric functions take angles as input, so we interpret $\frac{\sqrt{3}}{2}$ as an angle in radians.\n\n4. Since $\cos(x)$ for arbitrary $x$ can be evaluated using a calculator or series expansion, but here we just express the answer as $\sec\left(\frac{\sqrt{3}}{2}\right) = \frac{1}{\cos\left(\frac{\sqrt{3}}{2}\right)}$.\n\n5. Therefore, the exact value is $\boxed{\sec\left(\frac{\sqrt{3}}{2}\right) = \frac{1}{\cos\left(\frac{\sqrt{3}}{2}\right)}}$.\n\n6. If a decimal approximation is needed, use a calculator to find $\cos\left(\frac{\sqrt{3}}{2}\right) \approx 0.8776$, so $\sec\left(\frac{\sqrt{3}}{2}\right) \approx 1.139$.