\( 1 \leftarrow \) Find the exact value of each of the remaining trigonometric functions of \( \theta \), Rationalize denominators when applicable. \( \tan \theta=\frac{4}{3} \), given that \( \theta \) is in quadrant I Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sin \theta=\square \) (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression.) B. The function is undefined.

To find the exact values of the remaining trigonometric functions given \( \tan \theta = \frac{4}{3} \), we can use the relationship between the sides of a right triangle. Here, we can consider a right triangle where the opposite side to \( \theta \) is 4 and the adjacent side is 3. Using the Pythagorean theorem, the hypotenuse \( r \) can be calculated as follows: \[ r = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5. \] Now, we can find the sine and cosine functions as follows: 1. \( \sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{4}{5} \). 2. \( \cos \theta = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{3}{5} \). Now we can derive the remaining trigonometric functions: 3. \( \sec \theta = \frac{1}{\cos \theta} = \frac{5}{3} \). 4. \( \csc \theta = \frac{1}{\sin \theta} = \frac{5}{4} \). 5. \( \cot \theta = \frac{1}{\tan \theta} = \frac{3}{4} \). So, for the answer choices: A. \( \sin \theta = \frac{4}{5} \) and \( \cos \theta = \frac{3}{5} \) with other functions also found. The answer to complete your choice is: A. \( \sin \theta = \frac{4}{5} \). Now you have a full set of trigonometric functions based on a simple triangle! How cool is that?