Question

Given x equals pi over 3 comma what is the exact value of cosine of the quantity 2 times pi minus x end quantity question mark

Answer 1

Given:

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

We are required to find:

$\cos (2\pi\text{ - x)}$

We simply substitute the value of x into the cosine expression:

$\begin{gathered} =\text{ cos(2}\pi\text{ - }\frac{\pi}{3}) \\ =\text{ cos(}\frac{6\pi-\pi}{3}) \\ =\text{ cos(}\frac{5\pi}{3}) \end{gathered}$

The exact value of cos(2pi - x):

$\begin{gathered} =\text{ cos(}\frac{5\pi}{3}) \\ =cos300^0 \\ =\text{ }\frac{1}{2} \end{gathered}$

Answer: Option A