Answer
Yes, ($\frac{\sqrt 11}{6},\frac{5}{6}$) is a point on the unit circle.
Work Step by Step
Since ($\frac{\sqrt 11}{6},\frac{5}{6}$) is an (x, y) coordinate we can plug it into the equation of a circle, $x^{2}+y^{2}=1$.
$$(\frac{\sqrt 11}{6})^{2}+(\frac{5}{6})^{2}=1$$ $$\frac{\sqrt 11\times\sqrt 11}{6\times6}+\frac{5\times5}{6\times6}=1$$ $$\frac{11}{36}+\frac{25}{36}=1$$ $$\frac{36}{36}=1$$ We end up with 1=1, which is true. Therefore, ($\frac{\sqrt 11}{6},\frac{5}{6}$) is a point on the unit circle.