Find the exact value of each of the six trigonometric functions of $\theta$, if $(4,1)$ is a point on the terminal side of angle $\theta$.
\[
\sin \theta=
\]
(Simplify your antwer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators.)

Step 1 ：\( r = \sqrt{(x^2) + (y^2)} = \sqrt{(4^2) + (1^2)} = \sqrt{16 + 1} = \sqrt{17} \)

Step 2 ：\( \sin \theta = \frac{y}{r} = \frac{1}{\sqrt{17}} = \frac{\sqrt{17}}{17} \)

Step 3 ：\( \cos \theta = \frac{x}{r} = \frac{4}{\sqrt{17}} = \frac{4\sqrt{17}}{17} \)

Step 4 ：\( \tan \theta = \frac{y}{x} = \frac{1}{4} \)

Step 5 ：\( \csc \theta = \frac{r}{y} = \frac{\sqrt{17}}{1} = \sqrt{17} \)

Step 6 ：\( \sec \theta = \frac{r}{x} = \frac{\sqrt{17}}{4} \)

Step 7 ：\( \cot \theta = \frac{x}{y} = \frac{4}{1} = 4 \)

Step 8 ：\( \boxed{\sin \theta = \frac{\sqrt{17}}{17}, \cos \theta = \frac{4\sqrt{17}}{17}, \tan \theta = \frac{1}{4}, \csc \theta = \sqrt{17}, \sec \theta = \frac{\sqrt{17}}{4}, \cot \theta = 4} \)