give the exact value.\n2) \\( \\cos 210 ^ { \\circ } \\)\na) \\( - \\frac { \\sqrt { 3 } } { 2 } \\)\nb) \\(…

give the exact value.\n2) \\( \\cos 210 ^ { \\circ } \\)\na) \\( - \\frac { \\sqrt { 3 } } { 2 } \\)\nb) \\( \\frac { \\sqrt { 2 } } { 2 } \\)\nc) \\( \\frac { \\sqrt { 3 } } { 2 } \\)\nd) \\( - \\frac { \\sqrt { 2 } } { 2 } \\)

give the exact value.\n2) \\( \\cos 210 ^ { \\circ } \\)\na) \\( - \\frac { \\sqrt { 3 } } { 2 } \\)\nb) \\( \\frac { \\sqrt { 2 } } { 2 } \\)\nc) \\( \\frac { \\sqrt { 3 } } { 2 } \\)\nd) \\( - \\frac { \\sqrt { 2 } } { 2 } \\)

Answer

Explanation:

Step1: Determine the reference angle

The angle (210^{\circ}) is in the third quadrant. The reference angle (\theta_{r}=210^{\circ}- 180^{\circ}=30^{\circ}).

Step2: Use the cosine function property in the third quadrant

In the third quadrant, (\cos\theta<0). And we know that (\cos30^{\circ}=\frac{\sqrt{3}}{2}). So (\cos210^{\circ}=-\cos30^{\circ})

Answer:

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