Question

Use the circle unit to evaluate cos(23/6)

Answer 1

Given

`\begin{gathered} \cos \text{ }(23\pi)/(6) \\ A\text{ complete revolution in a circle is 2}\pi \\ We\text{ have to re-write }(23\pi)/(6)\text{ in such a way that it will not be more than 2}\pi\text{ } \\ \text{Hence, } \\ cos(23\pi)/(6)\text{ = cos(}(23\pi)/(6)-(24\pi)/(6)) \\ \cos \text{(}(23\pi)/(6))\text{ = cos(}(-\pi)/(6)) \end{gathered}`

The representation on the unit circle is shown below

Going round the circle in the negative direction, we realize

`\cos ((-\pi)/(6))\text{ = cos(}(11\pi)/(6))\text{ = }\frac{\sqrt[]{3}}{2}`
`\text{The answer is }\frac{\sqrt[]{3}}{2}`