Question

give the exact value.

1. \\( \cos 210 ^ { \circ } \\)

a) \\( - \frac { \sqrt { 3 } } { 2 } \\)
b) \\( \frac { \sqrt { 2 } } { 2 } \\)
c) \\( \frac { \sqrt { 3 } } { 2 } \\)
d) \\( - \frac { \sqrt { 2 } } { 2 } \\)

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:

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