Use reference angles to find the exact value of the following expression. Do not use a calculator. \[ \begin{array}{l}\sin \left(-300^{\circ}\right) \\ \text { A. select the correct choice below and, if necessary, fill in the answer box to complete your choice. } \\ \text { (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractions fo } \\ \text { the denominator.) } \\ \text { B. The answer is undefined. }\end{array} \]

To find the exact value of \( \sin(-300^\circ) \) using reference angles, we can follow these steps: 1. Find the reference angle for \( -300^\circ \). 2. Determine the sign of the sine function based on the quadrant in which the angle lies. 3. Calculate the exact value of the sine function using the reference angle. Let's start by finding the reference angle for \( -300^\circ \): The reference angle for \( -300^\circ \) is the positive acute angle formed by the terminal side of \( -300^\circ \) and the x-axis. To find this angle, we can add \( 360^\circ \) to \( -300^\circ \) to get an equivalent positive angle: \[ -300^\circ + 360^\circ = 60^\circ \] So, the reference angle for \( -300^\circ \) is \( 60^\circ \). Next, we determine the sign of the sine function based on the quadrant in which the angle lies. Since \( -300^\circ \) is in the fourth quadrant, the sine function is negative in the fourth quadrant. Therefore, the exact value of \( \sin(-300^\circ) \) is \( -\sin(60^\circ) \). Now, we calculate the exact value of \( \sin(60^\circ) \): \[ \sin(60^\circ) = \frac{\sqrt{3}}{2} \] So, the exact value of \( \sin(-300^\circ) \) is \( -\frac{\sqrt{3}}{2} \). Therefore, the answer is \( -\frac{\sqrt{3}}{2} \).