Question

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

Answer 1

We know that $\mathrm{pi}={180}^0$

$\cos \left(\frac{2\mathrm{pi}}{3}\right)=$ $\cos \left(\frac{2\times {180}^0}{3}\right)$

$=\cos (2\times {60}^0)$

$=\cos {120}^0$

We can find $\cos {120}^0$ using complementary form $\cos {90}^0$ and also using supplementary form $\cos {180}^0$.

$\cos {120}^0=$$\cos ({180}^0-{120}^0)$

$=-\cos {60}^0$ $\left[\cos \right({180}^0-\mathrm{\theta })=-\mathrm{cos\theta }]$

$=-\frac{1}{2}$ $[\cos {60}^0=\frac{1}{2}]$

⇒$\cos {120}^0=\frac{-1}{2}$

Hence, the required answer is $\frac{-1}{2}$ .