2 multiple choice 1 point\ngive the exact value.\n$\\cos 210^{\\circ}$\n$\\frac{\\sqrt{3}}{2}$\n$-\\frac{\\sq…

2 multiple choice 1 point\ngive the exact value.\n$\\cos 210^{\\circ}$\n$\\frac{\\sqrt{3}}{2}$\n$-\\frac{\\sqrt{2}}{2}$\n$\\frac{\\sqrt{2}}{2}$\n$-\\frac{\\sqrt{3}}{2}$

2 multiple choice 1 point\ngive the exact value.\n$\\cos 210^{\\circ}$\n$\\frac{\\sqrt{3}}{2}$\n$-\\frac{\\sqrt{2}}{2}$\n$\\frac{\\sqrt{2}}{2}$\n$-\\frac{\\sqrt{3}}{2}$

Answer

Explanation:

Step1: Determine the reference angle

Since (210^{\circ}=180^{\circ} + 30^{\circ}), the reference angle (\theta'=210^{\circ}-180^{\circ}=30^{\circ})

Step2: Determine the sign of the cosine function

The angle (210^{\circ}) is in the third - quadrant. In the third - quadrant, (\cos\theta=\frac{x}{r}) (where (x<0) and (r > 0)), so (\cos210^{\circ}<0)

Step3: Use the cosine of the reference angle

We know that (\cos30^{\circ}=\frac{\sqrt{3}}{2}). Using the formula (\cos(180^{\circ}+\alpha)=-\cos\alpha) (here (\alpha = 30^{\circ})), we have (\cos210^{\circ}=-\cos30^{\circ})

Answer:

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