Watch the video and then solve the problem given below. Click here to watch the video. Find the exact value of each of the remaining trigonometric functions of $\theta$. Rationalize denominators when applicable. $\sin \theta=\frac{\sqrt{5}}{10}$, given that $\cos \theta<0$ 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.

Step 1 ：Given that $\sin \theta = \frac{\sqrt{5}}{10}$, we can find $\sin^2 \theta$ as follows:

Step 2 ：$\sin^2 \theta = \left(\frac{\sqrt{5}}{10}\right)^2 = \frac{5}{100}$

Step 3 ：Using the Pythagorean identity $\sin^2 \theta + \cos^2 \theta = 1$, we can find $\cos^2 \theta$:

Step 4 ：$\cos^2 \theta = 1 - \sin^2 \theta = 1 - \frac{5}{100} = \frac{95}{100}$

Step 5 ：Since $\cos \theta < 0$, we can find the value of $\cos \theta$ as follows:

Step 6 ：$\cos \theta = -\sqrt{\cos^2 \theta} = -\sqrt{\frac{95}{100}} = -\frac{\sqrt{95}}{10}$

Step 7 ：\(\boxed{\cos \theta = -\frac{\sqrt{95}}{10}}\)