1. The problem asks for the x-coordinate of point A on a circle centered at the origin with radius 1, where point A is located at an angle $\frac{\pi}{5}$ radians above the negative x-axis. 2. The formula for the coordinates of a point on a unit circle at an angle $\theta$ from the positive x-axis is: $$ (x, y) = (\cos \theta, \sin \theta) $$ 3. Since point A is $\frac{\pi}{5}$ radians above the negative x-axis, its angle from the positive x-axis is: $$ \pi + \frac{\pi}{5} = \frac{5\pi}{5} + \frac{\pi}{5} = \frac{6\pi}{5} $$ 4. Therefore, the x-coordinate of point A is: $$ x = \cos \left( \frac{6\pi}{5} \right) $$ 5. Among the answer choices, this corresponds to option D: $\cos(6\pi/5)$. Final answer: The x-coordinate of point A is $\cos \left( \frac{6\pi}{5} \right)$.