Use reference angles to find the exact value of the following expression. Do not use a calculator. \( \sin \left(-210^{\circ}\right) \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \sin \left(-210^{\circ}\right)=\square \)

1. Recognize that angles differing by multiples of \(360^\circ\) are coterminal. Since \[ -210^\circ + 360^\circ = 150^\circ, \] we have \[ \sin\left(-210^\circ\right) = \sin\left(150^\circ\right). \] 2. Identify the reference angle for \(150^\circ\). Since \(150^\circ\) is in the second quadrant, \[ \text{reference angle} = 180^\circ - 150^\circ = 30^\circ. \] 3. Recall that in the second quadrant the sine function is positive and that \[ \sin(30^\circ) = \frac{1}{2}. \] Therefore, \[ \sin(150^\circ)=\frac{1}{2}. \] 4. Conclude that \[ \sin\left(-210^\circ\right)=\frac{1}{2}. \] A. \( \sin \left(-210^{\circ}\right)=\frac{1}{2} \)