Question

Given x=pi/3, what is the exact value of cos(pi+x)?A. 1/2B. - square root of 3/2C. square root of 3/2D. -1/2

Answer 1

SOLUTION

The given value is:

$x=\frac{\pi}{3}$

It follows that:

$\cos(\pi+x)=\cos(\pi+\frac{\pi}{3})$

This gives:

$\begin{gathered} \cos(\pi+\frac{\pi}{3}) \\ =\cos(\frac{3\pi+\pi}{3}) \\ =\cos(\frac{4\pi}{3}) \\ =-\frac{1}{2} \end{gathered}$

Therefore the correct answer is option D