Given:
[tex]\begin{gathered} \frac{3\pi}{4} \\ \pi \\ \frac{7\pi}{6} \\ \frac{5\pi}{3} \\ \frac{7\pi}{4} \\ \frac{4\pi}{3} \\ \frac{3\pi}{2} \\ 2\pi \end{gathered}[/tex]
To arrange the angles in increasing order, we first get the value of their cosines as shown below:
[tex]cos\frac{3\pi}{4}=-\frac{\sqrt{2}}{2}[/tex][tex]cos\pi=-1[/tex][tex]cos\frac{7\pi}{6}=-\frac{\sqrt{3}}{2}[/tex][tex]cos\frac{5\pi}{3}=\frac{1}{2}[/tex][tex]cos\frac{7\pi}{4}=\frac{\sqrt{2}}{2}[/tex][tex]cos\frac{4\pi}{3}=-\frac{1}{2}[/tex][tex]cos\frac{3\pi}{2}=0[/tex][tex]cos2\pi=1[/tex]
Therefore, the angles in increasing order of their cosines are:
[tex]\pi<\frac{7\pi}{6}<\frac{3\pi}{4}<\frac{4\pi}{3}<\frac{3\pi}{2}<\frac{5\pi}{3}<\frac{7\pi}{4}<2\pi[/tex]
