B. The function is undefined. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. \( \cos \theta=\frac{3 \sqrt{73}}{73} \) (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. \( \tan \theta=\frac{8}{3} \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. sec \( \theta=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function is undefined. (Sle ample Get more help a

Let's analyze the given information and solve for the required trigonometric functions step by step. ### Given: \[ \cos \theta = \frac{3\sqrt{73}}{73} \] ### 1. Finding \(\tan \theta\) We know that: \[ \tan \theta = \frac{\sin \theta}{\cos \theta} \] First, we need to find \(\sin \theta\). Using the Pythagorean identity: \[ \sin^2 \theta + \cos^2 \theta = 1 \] \[ \sin^2 \theta = 1 - \cos^2 \theta \] \[ \cos^2 \theta = \left(\frac{3\sqrt{73}}{73}\right)^2 = \frac{9 \times 73}{73^2} = \frac{9}{73} \] \[ \sin^2 \theta = 1 - \frac{9}{73} = \frac{64}{73} \] \[ \sin \theta = \frac{8}{\sqrt{73}} = \frac{8\sqrt{73}}{73} \] Now, calculate \(\tan \theta\): \[ \tan \theta = \frac{\sin \theta}{\cos \theta} = \frac{\frac{8\sqrt{73}}{73}}{\frac{3\sqrt{73}}{73}} = \frac{8}{3} \] **Answer for \(\tan \theta\):** \[ \boxed{\tan \theta = \frac{8}{3}} \] ### 2. Finding \(\sec \theta\) \(\sec \theta\) is the reciprocal of \(\cos \theta\): \[ \sec \theta = \frac{1}{\cos \theta} = \frac{73}{3\sqrt{73}} = \frac{73}{3\sqrt{73}} \times \frac{\sqrt{73}}{\sqrt{73}} = \frac{73\sqrt{73}}{3 \times 73} = \frac{\sqrt{73}}{3} \] **Answer for \(\sec \theta\):** \[ \boxed{\sec \theta = \frac{\sqrt{73}}{3}} \] ### Summary of Choices: - **A.** \( \tan \theta = \frac{8}{3} \) **✓ Correct** - **B.** The function is undefined. **✗ Incorrect** - **A.** \( \sec \theta = \frac{\sqrt{73}}{3} \) **✓ Correct** - **B.** The function is undefined. **✗ Incorrect** If you have any further questions or need additional clarifications, feel free to ask!