Title: Cosine Value Calculation---**Problem Description:**Find the exact value of \( \cos \, \alpha \) given that \( \sin \, \alpha = \frac{7}{11} \) and \( \alpha \) is in quadrant I.\[ \cos \, \alpha = \boxed{} \]*(Simplify your answer. Type an exact answer, using radicals as needed.)***Instructions:**1. Enter your answer in the answer box provided and then click "Check Answer."---**Explanation:**To find the cosine of the angle \( \alpha \), we use the relationship between the sine and cosine in a right triangle as well as trigonometric identities.Given:\[ \sin \, \alpha = \frac{7}{11} \]Since \( \alpha \) is in quadrant I, both sine and cosine values will be positive.We know the fundamental trigonometric identity:\[ \sin^2 \alpha + \cos^2 \alpha = 1 \]First, we square the given sine value:\[ \left(\frac{7}{11}\right)^2 = \frac{49}{121} \]Then, we use the identity to solve for \( \cos^2 \alpha \):\[ \cos^2 \alpha = 1 - \sin^2 \alpha \]\[ \cos^2 \alpha = 1 - \frac{49}{121} \]\[ \cos^2 \alpha = \frac{121}{121} - \frac{49}{121} \]\[ \cos^2 \alpha = \frac{72}{121} \]Next, we take the square root to find \( \cos \, \alpha \):\[ \cos \alpha = \sqrt{\frac{72}{121}} \]\[ \cos \alpha = \frac{\sqrt{72}}{11} \]\[ \cos \alpha = \frac{6\sqrt{2}}{11} \]Therefore, the exact value of \( \cos \alpha \) is:\[ \cos \alpha = \frac{6\sqrt{2}}{11} \]*[Please input your answer in the box provided and check to confirm it's correct.]*

Name: Title: Cosine Value Calculation---**Problem Description:**Find the ex
Uploaded: 2024-03-20T06:46:55.000Z
Channel: Bartleby
Description: Title: Cosine Value Calculation---**Problem Description:**Find the exact value of \( \cos \, \alpha \) given that \( \sin \, \alpha = \frac{7}{11} \) and \( \alpha \) is in quadrant I.\[ \cos \, \alpha = \boxed{} \]*(Simplify your answer. Type an ex