Solution
To find coterminal angles we add 2pi n
to the angle, where n is some integer, positive, negative, or zero.
Therefore when we find n, the answer will be
[tex]\frac{44\pi}{9}+2\pi\cdot n[/tex]Since we want the coterminal angle to be between 0 and 2pi,
we write an inequality which indicates that:
[tex]\begin{gathered} 0<\frac{44\pi}{9}+2\pi\cdot n<2\pi \\ \text{ Dividing all through by }\pi \\ \Rightarrow0<\frac{44}{9}+2\cdot n<2 \\ \text{ Multiply all through by }9 \\ \Rightarrow0<44+18n<18 \\ \\ \Rightarrow-44<18n<18-44 \\ \\ \Rightarrow-44<18n<-26 \\ \Rightarrow-\frac{22}{9}when n = -1[tex]\Rightarrow\frac{44\pi}{9}+2\pi\cdot n=\frac{44\pi}{9}-2\pi=\frac{26}{9}\pi[/tex]Hence, the value of a is 26
and the value of b is 9