Find the exact value of each of the remaining tigonometrie functions of 0 . Rationalize denominatore when applicable. \( \tan 0=\frac{4}{3} \), given that 0 is in quadrant । (Simplify your answer, including any radicals. Use integers of fractions for any numbers in the expression.) II. The function la undefined, Select the correct oholee below and, if necessary, fill in the answer box to complete your choice. A. \( \operatorname{coc} 0=\frac{5}{4} \) (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. \( \sec 0=\frac{5}{3} \) (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. \( \cot 0= \) \( \square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function is undefined. View an example Get more help * MacBook Air

Given that \(\tan \theta = \frac{4}{3}\) and \(\theta\) is in the **first quadrant**, we can determine the remaining trigonometric functions using a right triangle approach. ### Step 1: Determine the Sides of the Triangle Since \(\tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{4}{3}\), we can consider: - **Opposite side**: 4 - **Adjacent side**: 3 Using the Pythagorean theorem: \[ \text{Hypotenuse} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] ### Step 2: Find the Remaining Trigonometric Functions 1. **Cosecant (\(\csc \theta\))**: \[ \csc \theta = \frac{\text{Hypotenuse}}{\text{Opposite}} = \frac{5}{4} \] **Answer**: \[ \boxed{\csc \theta = \frac{5}{4}} \] **Choice**: A. \( \csc \theta = \frac{5}{4} \) 2. **Secant (\(\sec \theta\))**: \[ \sec \theta = \frac{\text{Hypotenuse}}{\text{Adjacent}} = \frac{5}{3} \] **Answer**: \[ \boxed{\sec \theta = \frac{5}{3}} \] **Choice**: A. \( \sec \theta = \frac{5}{3} \) 3. **Cotangent (\(\cot \theta\))**: \[ \cot \theta = \frac{\text{Adjacent}}{\text{Opposite}} = \frac{3}{4} \] **Answer**: \[ \boxed{\cot \theta = \frac{3}{4}} \] **Choice**: A. \( \cot \theta = \frac{3}{4} \) ### Summary of All Trigonometric Functions \[ \begin{align*} \sin \theta &= \frac{4}{5} \\ \cos \theta &= \frac{3}{5} \\ \tan \theta &= \frac{4}{3} \\ \csc \theta &= \frac{5}{4} \\ \sec \theta &= \frac{5}{3} \\ \cot \theta &= \frac{3}{4} \\ \end{align*} \] All functions are **defined** in the first quadrant, so there is no need to select the option stating the function is undefined.