To determine the exact value of [tex]\(\cos 60^{\circ}\)[/tex], we begin by recalling the values of cosine for common angles on the unit circle.
The unit circle is a circle with a radius of 1 centered at the origin of a coordinate plane. Angles measured from the positive x-axis corresponding to the values we encounter frequently in trigonometry include [tex]\(0^\circ\)[/tex], [tex]\(30^\circ\)[/tex], [tex]\(45^\circ\)[/tex], [tex]\(60^\circ\)[/tex], and [tex]\(90^\circ\)[/tex].
For the angle [tex]\(60^{\circ}\)[/tex], it is helpful to remember the trigonometric values associated with this specific angle. The cosine function represents the x-coordinate of the point where the terminal side of the angle intersects the unit circle.
By definition:
[tex]\[ \cos 60^{\circ} = \frac{1}{2} \][/tex]
Therefore, the exact value of [tex]\(\cos 60^{\circ}\)[/tex] is [tex]\(\frac{1}{2}\)[/tex].
We match this with the options provided:
0
[tex]\[\frac{1}{2}\][/tex]
[tex]\[\frac{\sqrt{2}}{2}\][/tex]
[tex]\[\frac{\sqrt{3}}{2}\][/tex]
The correct answer is:
[tex]\(\frac{1}{2}\)[/tex]
