.2 Give the exact value. \[ \cos \left(150^{\circ}\right) \] A. \( \frac{\sqrt{3}}{2} \) B. \( \frac{\sqrt{2}}{2} \) c. \( -\frac{\sqrt{2}}{2} \) D. \( -\frac{\sqrt{3}}{2} \)

To find the exact value of \(\cos(150^\circ)\), let's use the unit circle and trigonometric identities. 1. **Reference Angle:** \(150^\circ\) is in the **second quadrant**. The reference angle (\(\theta\)) for \(150^\circ\) is: \[ \theta = 180^\circ - 150^\circ = 30^\circ \] 2. **Cosine in the Second Quadrant:** In the second quadrant, the cosine values are **negative**. 3. **Exact Value:** \[ \cos(150^\circ) = -\cos(30^\circ) = -\frac{\sqrt{3}}{2} \] **Answer:** **D.** \( -\frac{\sqrt{3}}{2} \)