Question

Given x = pi/3, what is the exact value of cos (pi+x)?

Answer 1

$\begin{gathered} x=\frac{\pi}{3} \\ \\ \cos (\pi+x)=cos(\pi+\frac{\pi}{3})=\cos (\frac{4\pi}{3}) \end{gathered}$

Using the unit circle above you can identify the cosine as the x-coordinate.

Then, the cosine of (4pi/3) is -1/2