Complete the table with exact trigonometric function values for theta = 60 degrees.

1. Identify the known values: The problem provides a table where $\theta = 60^{\circ}$. We are given the values for $\cos(60^{\circ}) = \frac{1}{2}$ and $\tan(60^{\circ}) = \sqrt{3}$, and $\sec(60^{\circ}) = 2$. We need to find $\sin(60^{\circ})$, $\cot(60^{\circ})$, and $\csc(60^{\circ})$.
2. Calculate $\sin(60^{\circ})$: We know the Pythagorean identity $\sin^2(\theta) + \cos^2(\theta) = 1$. Substituting the value of $\cos(60^{\circ})$:
$$ \sin^2(60^{\circ}) + \left(\frac{1}{2}\right)^2 = 1 $$
$$ \sin^2(60^{\circ}) + \frac{1}{4} = 1 $$
$$ \sin^2(60^{\circ}) = 1 - \frac{1}{4} $$
$$ \sin^2(60^{\circ}) = \frac{3}{4} $$
Taking the square root of both sides (and considering that for $60^{\circ}$, sine is positive):
$$ \sin(60^{\circ}) = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2} $$
3. Calculate $\cot(60^{\circ})$: The cotangent is the reciprocal of the tangent, $\cot(\theta) = \frac{1}{\tan(\theta)}$.
$$ \cot(60^{\circ}) = \frac{1}{\tan(60^{\circ})} = \frac{1}{\sqrt{3}} $$
4. Calculate $\csc(60^{\circ})$: The cosecant is the reciprocal of the sine, $\csc(\theta) = \frac{1}{\sin(\theta)}$.
$$ \csc(60^{\circ}) = \frac{1}{\sin(60^{\circ})} = \frac{1}{\frac{\sqrt{3}}{2}} = \frac{2}{\sqrt{3}} $$
5. Fill in the table: Based on the calculations, the missing values are $\sin(60^{\circ}) = \frac{\sqrt{3}}{2}$, $\cot(60^{\circ}) = \frac{1}{\sqrt{3}}$, and $\csc(60^{\circ}) = \frac{2}{\sqrt{3}}$.