[tex]\begin{gathered} \text{Given} \\ \frac{35\pi}{9} \\ \text{Find coterminal angle in the interval }(0,2\pi) \end{gathered}[/tex]
Subtract 2π to the given angle as it is equivalent to one revolution.
[tex]\begin{gathered} \frac{35\pi}{9}-2\pi \\ \frac{35\pi}{9}-\frac{18\pi}{9} \\ =\frac{17\pi}{9} \\ \\ \text{Subtracting further by }2\pi\text{ will result with coterminal angles outside the interval }(0,2\pi) \\ \\ \text{therefore, the coterminal angle of }\frac{35\pi}{9}\text{ in the interval }(0,2\pi)\text{ is } \\ \frac{17\pi}{9} \end{gathered}[/tex]
