Answer:
[F] [tex]\cos\left(\frac{2\pi}{3}\right)[/tex]
Step-by-step explanation:
Remember that on a unit circle, cosine represents the x-coordinates, and sine represents the y-coordinate. Since the question is asking for the x- coordinate, the function we are looking for is cosine.
Solving:
[tex]\begin{itemize} \item The equation of the unit circle is \(x^2 + y^2 = 1\). \item For any point on the unit circle corresponding to an angle \(\theta\), the coordinates are \((\cos(\theta), \sin(\theta))\).\end{itemize}[/tex]
Remember, the point (1,0) on the unit circle has a radian value of π/2 and the distance from that point is π/6 radians.
[tex]\theta = \frac{\pi}{2} + \frac{\pi}{6} = \boxed{\frac{2\pi}{3} }[/tex]
[tex]\text{Given}~ \(\theta = \frac{2\pi}{3}\), the coordinates of point \(A\) are:\[\left(\cos\left(\frac{2\pi}{3}\right), \sin\left(\frac{2\pi}{3}\right)\right)\][/tex]
[tex]\text{Since we are looking for the x-value}:\\\\\[\boxed{x = \cos\left(\frac{2\pi}{3}\right)}\][/tex]
Therefore, the correct answer choice is F.
