1. The problem asks for the x-coordinate of point A, which lies on a circle centered at the origin with radius 1. 2. Point A is in the second quadrant, and the angle between the positive x-axis and the line segment from the origin to A is $\frac{\pi}{5}$ radians. 3. The formula for the coordinates of a point on a circle of radius $r$ at an angle $\theta$ from the positive x-axis is: $$x = r \cos(\theta), \quad y = r \sin(\theta)$$ 4. Since the radius $r = 1$, the x-coordinate of point A is: $$x = \cos\left(\frac{\pi}{5}\right)$$ 5. However, point A is in the second quadrant where x-values are negative, so: $$x = -\cos\left(\frac{\pi}{5}\right)$$ 6. Evaluating $\cos\left(\frac{\pi}{5}\right)$ numerically: $$\cos\left(\frac{\pi}{5}\right) \approx 0.8090$$ 7. Therefore, the x-coordinate of point A is approximately: $$x \approx -0.8090$$ Final answer: The x-coordinate of point A is $-\cos\left(\frac{\pi}{5}\right) \approx -0.8090$.