Answer:
[tex]\frac{3\pi}{4} <\pi <\frac{7\pi}{6}<\frac{4\pi}{3}<\frac{3\pi}{2}<\frac{5\pi}{3}<\frac{7\pi}{4}<2\pi[/tex]
Step-by-step explanation:
we are given different angles
we can see that each angles have different denominators
so, firstly we will find common denominators
denominators are 1 , 2,3,4,6
so, LCD will be 12
now, we will make denominator of all terms 12
[tex]\frac{3\pi}{4} =\frac{3\pi\times 3}{4\times 3}=\frac{9\pi}{12}[/tex]
[tex]\pi =\frac{\pi\times 12}{1\times 12}=\frac{12\pi}{12}[/tex]
[tex]\frac{7\pi}{6} =\frac{7\pi\times 2}{6\times 2}=\frac{14\pi}{12}[/tex]
[tex]\frac{5\pi}{3} =\frac{5\pi\times 4}{3\times 4}=\frac{20\pi}{12}[/tex]
[tex]\frac{7\pi}{4} =\frac{7\pi\times 3}{4\times 3}=\frac{21\pi}{12}[/tex]
[tex]\frac{4\pi}{3} =\frac{4\pi\times 4}{3\times 4}=\frac{16\pi}{12}[/tex]
[tex]\frac{3\pi}{2} =\frac{3\pi\times 6}{2\times 6}=\frac{18\pi}{12}[/tex]
[tex]2\pi =\frac{2\pi\times 12}{1\times 12}=\frac{24\pi}{12}[/tex]
we can see that denominators are same
so, we can arrange it according to numerators as
[tex]\frac{9\pi}{12} <\frac{12\pi}{12}<\frac{14\pi}{12}<\frac{16\pi}{12}<\frac{18\pi}{12}<\frac{20\pi}{12}<\frac{21\pi}{12}<\frac{24\pi}{12}[/tex]
we can replace values
and we get order as
[tex]\frac{3\pi}{4} <\pi <\frac{7\pi}{6}<\frac{4\pi}{3}<\frac{3\pi}{2}<\frac{5\pi}{3}<\frac{7\pi}{4}<2\pi[/tex]
