Question

Find the value of cos $(2\mathrm{\pi }/3)$

Answer 1

Finding the value of $\cos \frac{2\mathrm{\pi }}{3}$

$\cos \frac{2\mathrm{\pi }}{3}=\cos \frac{2\times {180}^{\circ }}{3}$ ; $[\because \pi =180°]$

$=\cos 120°$

$120°$ can be represented in terms of two angles i.e. either $90°$ or $180°$

$$\begin{gathered} \cos 120°=\cos (180°–60°) \\ =–\cos 60° \\ =-\frac{1}{2} \end{gathered}$$

Hence the value of $\cos \frac{2\mathrm{\pi }}{3}$ is $-\frac{1}{2}$