Answer:
1/2
Explanation:
In the unit circle, the pair (x,y) is defined below:
[tex](x,y)=(\frac{1}{2},-\frac{\sqrt[]{3}}{2})[/tex]First, we find the value of r, the hypotenuse.
[tex]\begin{gathered} r^2=x^2+y^2 \\ r^2=(\frac{1}{2})^2+(-\frac{\sqrt[]{3}}{2})^2 \\ r^2=\frac{1}{4}+\frac{3}{4} \\ r^2=\frac{4}{4} \\ r^2=1 \\ r=1 \end{gathered}[/tex]We then evaluate the value of cos 5pi/3.
[tex]\begin{gathered} \cos \theta=\frac{x}{r} \\ \text{Therefore:} \\ \cos \frac{5\pi}{3}=\frac{1}{2}\div1 \\ \cos \frac{5\pi}{3}=\frac{1}{2} \end{gathered}[/tex]