Find the exact value of each of the six trigonometric functions of the angle $\theta$ in the figure.
\[
\sin \theta=\frac{1}{\sqrt{5}}
\]

Step 1 ：Given that \(\sin \theta = \frac{1}{\sqrt{5}}\)

Step 2 ：Use the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\) to find \(\cos \theta\)

Step 3 ：\(\cos \theta = \sqrt{1 - \sin^2 \theta} = \sqrt{1 - \left(\frac{1}{\sqrt{5}}\right)^2} = \frac{2}{\sqrt{5}}\)

Step 4 ：Use the definitions of the other trigonometric functions in terms of \(\sin \theta\) and \(\cos \theta\) to find their values

Step 5 ：\(\tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{\frac{1}{\sqrt{5}}}{\frac{2}{\sqrt{5}}} = \frac{1}{2}\)

Step 6 ：\(\csc \theta = \frac{1}{\sin \theta} = \sqrt{5}\)

Step 7 ：\(\sec \theta = \frac{1}{\cos \theta} = \frac{\sqrt{5}}{2}\)

Step 8 ：\(\cot \theta = \frac{1}{\tan \theta} = 2\)

Step 9 ：Final Answer: \(\boxed{\sin \theta = \frac{1}{\sqrt{5}}, \cos \theta = \frac{2}{\sqrt{5}}, \tan \theta = \frac{1}{2}, \csc \theta = \sqrt{5}, \sec \theta = \frac{\sqrt{5}}{2}, \cot \theta = 2}\)