evaluate. write your answer in simplified, rationalized form. do not round. cos 150°

Explanation:

Step1: Use the cosine of supplementary angles formula

We know that (\cos(180^{\circ}-\theta)=-\cos\theta). Here (\theta = 30^{\circ}), so (\cos150^{\circ}=\cos(180^{\circ} - 30^{\circ})). By the formula (\cos(180^{\circ}-30^{\circ})=-\cos30^{\circ}).

Step2: Recall the value of (\cos30^{\circ})

We know that (\cos30^{\circ}=\frac{\sqrt{3}}{2}). Substituting the value of (\cos30^{\circ}) into (-\cos30^{\circ}), we get (-\frac{\sqrt{3}}{2}).

Answer:

(-\frac{\sqrt{3}}{2})