Given
[tex]\begin{gathered} \cos \text{ }\frac{23\pi}{6} \\ A\text{ complete revolution in a circle is 2}\pi \\ We\text{ have to re-write }\frac{23\pi}{6}\text{ in such a way that it will not be more than 2}\pi\text{ } \\ \text{Hence, } \\ cos\frac{23\pi}{6}\text{ = cos(}\frac{23\pi}{6}-\frac{24\pi}{6}) \\ \cos \text{(}\frac{23\pi}{6})\text{ = cos(}\frac{-\pi}{6}) \end{gathered}[/tex]The representation on the unit circle is shown below
Going round the circle in the negative direction, we realize
[tex]\cos (\frac{-\pi}{6})\text{ = cos(}\frac{11\pi}{6})\text{ = }\frac{\sqrt[]{3}}{2}[/tex][tex]\text{The answer is }\frac{\sqrt[]{3}}{2}[/tex]
