Use a reference angle to find the exact value of the following expression. Do not use a calculator. $$ \sin \left(120^{\circ}\right) $$ Select the correct choice below and, if necessary. Fill in the answer box to complete your choice. A. $$ \sin \left(120^{\circ}\right)=\square $$ (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Rationalize all denominators ) B. The undefined.

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To find the exact value of $$ \sin(120^\circ) $$, we can use the concept of reference angles.

1. **Identify the reference angle**: The angle $$ 120^\circ $$ is in the second quadrant. The reference angle is found by subtracting $$ 120^\circ $$ from $$ 180^\circ $$:
   $$
   180^\circ - 120^\circ = 60^\circ
   $$

2. **Determine the sine value**: In the second quadrant, the sine function is positive. Therefore:
   $$
   \sin(120^\circ) = \sin(60^\circ)
   $$

3. **Find the sine of the reference angle**: The exact value of $$ \sin(60^\circ) $$ is:
   $$
   \sin(60^\circ) = \frac{\sqrt{3}}{2}
   $$

Putting it all together, we have:
$$
\sin(120^\circ) = \frac{\sqrt{3}}{2}
$$

Thus, the answer is:
A. $$ \sin(120^\circ) = \frac{\sqrt{3}}{2} $$
A. $$ \sin(120^\circ) = \frac{\sqrt{3}}{2} $$

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