Find the exact value of each of the remaining trigonometric functions of $\theta$. Rationalize denominators when applicable. $\sin \theta=\frac{\sqrt{3}}{5}$ given that $\theta$ is in quadrant I

Step 1 ：We are given that \(\sin \theta = \frac{\sqrt{3}}{5}\) and \(\theta\) is in quadrant I.

Step 2 ：We can use the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\) to find the value of \(\cos \theta\).

Step 3 ：Since \(\theta\) is in quadrant I, \(\cos \theta\) will be positive.

Step 4 ：Solving for \(\cos \theta\) we get \(\cos \theta = \frac{4}{5}\).

Step 5 ：We can then find the other trigonometric functions using the definitions of those functions in terms of \(\sin \theta\) and \(\cos \theta\).

Step 6 ：We find that \(\tan \theta = \frac{\sqrt{3}}{4}\), \(\csc \theta = \frac{5\sqrt{3}}{3}\), \(\sec \theta = \frac{5}{4}\), and \(\cot \theta = \frac{4\sqrt{3}}{3}\).

Step 7 ：\(\boxed{\text{Final Answer: The exact values of the remaining trigonometric functions of } \theta \text{ are } \cos \theta = \frac{4}{5}, \tan \theta = \frac{\sqrt{3}}{4}, \csc \theta = \frac{5\sqrt{3}}{3}, \sec \theta = \frac{5}{4}, \text{ and } \cot \theta = \frac{4\sqrt{3}}{3}}\)