Find the exact value of each of the remaining trigonometric functions of \( \theta \). Rationalize denominators when applicable. \( \boldsymbol{\operatorname { t a n }} \theta=\frac{4}{3} \), given that \( \theta \) is in quadrant । Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sin \theta=\frac{4}{5} \) (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. \( \boldsymbol{\operatorname { c o s }} \theta=\frac{3}{5} \) (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. \( \boldsymbol{\operatorname { c s c }} \theta= \) \( \square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function is undefined. this View an example Get more help -

Given that \( \tan \theta = \frac{4}{3} \) and assuming \( \theta \) is in **Quadrant I** (where all trigonometric functions are positive), we can find the remaining trigonometric functions as follows: 1. **Determine \( \sin \theta \) and \( \cos \theta \):** - Since \( \tan \theta = \frac{\text{opposite}}{\text{adjacent}} = \frac{4}{3} \), we can construct a right triangle where the opposite side is 4 and the adjacent side is 3. - The hypotenuse \( r \) can be found using the Pythagorean theorem: \[ r = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \] - Therefore: \[ \sin \theta = \frac{\text{opposite}}{r} = \frac{4}{5} \] \[ \cos \theta = \frac{\text{adjacent}}{r} = \frac{3}{5} \] 2. **Determine \( \csc \theta \):** - \( \csc \theta \) is the reciprocal of \( \sin \theta \): \[ \csc \theta = \frac{1}{\sin \theta} = \frac{5}{4} \] **Final Answers:** - **For \( \sin \theta \):** - **A.** \( \sin \theta = \frac{4}{5} \) - **For \( \cos \theta \):** - **A.** \( \cos \theta = \frac{3}{5} \) - **For \( \csc \theta \):** - **A.** \( \csc \theta = \frac{5}{4} \) All functions are defined in Quadrant I, so option **B** (undefined) does not apply.