Question

17 multiple choice 1 point give the exact value, cos 210° -√3/2 √3/2 -√2/2 √2/2 previous

Explanation:

Step1: Determine the quadrant

\(210^{\circ}\) is in the third quadrant (\(180^{\circ}<210^{\circ}<270^{\circ}\)). In the third quadrant, the cosine function is negative.

Step2: Find the reference angle

The reference angle \(\theta_{r}=210^{\circ}- 180^{\circ}=30^{\circ}\).

Step3: Use the cosine value of the reference angle

We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\). Since \(\cos210^{\circ}\) is negative (from Step 1), \(\cos210^{\circ}=-\cos30^{\circ}\).

Answer:

\(-\frac{\sqrt{3}}{2}\) (assuming the first option is \(-\frac{\sqrt{3}}{2}\))