Find the exact value of each of the remaining trigonometric functions of $\theta$. Rationalize denominators when applicable.
$\sin \theta=\frac{\sqrt{5}}{7}$ given that $\theta$ is in quadrant II
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\cos \theta=$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\csc \theta=$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\sec \theta=$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)
B. The function is undefined.
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. $\tan \theta=$
(Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.)

Step 1 ：We are given that \(\sin \theta=\frac{\sqrt{5}}{7}\) and \(\theta\) is in quadrant II. We can use the Pythagorean identity \(\sin^2 \theta + \cos^2 \theta = 1\) to find \(\cos \theta\). Since \(\theta\) is in quadrant II, \(\cos \theta\) will be negative.

Step 2 ：Using the Pythagorean identity, we find that \(\cos \theta = -\sqrt{1 - \sin^2 \theta} = -\sqrt{1 - \left(\frac{\sqrt{5}}{7}\right)^2} = -\frac{\sqrt{44}}{7}\).

Step 3 ：The reciprocal of \(\sin \theta\) is \(\csc \theta\), so we can find \(\csc \theta\) by taking the reciprocal of \(\sin \theta\). This gives us \(\csc \theta = \frac{1}{\sin \theta} = \frac{7}{\sqrt{5}}\).

Step 4 ：Similarly, the reciprocal of \(\cos \theta\) is \(\sec \theta\), so we can find \(\sec \theta\) by taking the reciprocal of \(\cos \theta\). This gives us \(\sec \theta = \frac{1}{\cos \theta} = -\frac{7}{\sqrt{44}}\).

Step 5 ：Finally, \(\tan \theta\) is the ratio of \(\sin \theta\) to \(\cos \theta\), so we can find \(\tan \theta\) by dividing \(\sin \theta\) by \(\cos \theta\). This gives us \(\tan \theta = \frac{\sin \theta}{\cos \theta} = -\frac{\sqrt{5}}{\sqrt{44}}\).

Step 6 ：\(\boxed{\cos \theta = -\frac{\sqrt{44}}{7}}\)

Step 7 ：\(\boxed{\csc \theta = \frac{7}{\sqrt{5}}}\)

Step 8 ：\(\boxed{\sec \theta = -\frac{7}{\sqrt{44}}}\)

Step 9 ：\(\boxed{\tan \theta = -\frac{\sqrt{5}}{\sqrt{44}}}\)