Question

How do you find the exact value of $\cos \left(-\frac{2\mathrm{\pi }}{3}\right)$?

Answer 1

Compute the value of the given expression:

Given: $\cos \left(-\frac{2\mathrm{\pi }}{3}\right)$

using identity $\cos (-\theta )=\cos \left(\theta \right)$

$\cos \left(-\frac{2\mathrm{\pi }}{3}\right)=\cos \left(\frac{2\mathrm{\pi }}{3}\right)$

$\cos \left(\frac{2\mathrm{\pi }}{3}\right)=\cos \left(\mathrm{\pi }-\frac{\mathrm{\pi }}{3}\right)$

using identity $\cos (\mathrm{\pi }-\theta )=-\cos \left(\theta \right)$

$$\begin{gathered} \cos \left(\mathrm{\pi }-\frac{\mathrm{\pi }}{3}\right)=-\cos \left(\frac{\mathrm{\pi }}{3}\right) \\ \cos \left(\frac{2\mathrm{\pi }}{3}\right)=-\frac{1}{2} \end{gathered}$$

Therefore, the value of the given expression is $-\frac{1}{2}$.

Hence, the value of the expression $\cos \left(-\frac{2\mathrm{\pi }}{3}\right)$ is $-\frac{1}{2}$ .