Question

$\cos \frac{2\mathrm{\pi }}{3}=\_\_\_\_\_\_\_\_.$

Short answer

The value of$\cos \frac{2\mathrm{\pi }}{3}=-\frac{1}{2}.$

Step-by-step solution

Step 1. Given Information 

The cosine function is a periodic function. The ratio of the adjacent side to the hypotenuse of the right-angled triangle is called the cosine function.

Step 2. Filling the blank 

We can write $\cos \frac{2\mathrm{\pi }}{3}$as $\cos \left(\mathrm{\pi }-\frac{\mathrm{\pi }}{3}\right).$

As we know cosine function is negative in the second quadrant.

Thus,

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