Answer:
[tex] \csc( \theta) = \frac{19}{18} \\ \frac{1}{ \sin( \theta) } = \frac{19}{18} \\ \sin( \theta) = \frac{18}{19} \\ \theta = { \sin }^{ - 1} ( \frac{18}{19} ) \\ \theta = 71.3 \degree, \: 108.7 \degree, \: 288.7 \degree, \: 468.7 \degree, \: 648.7 \degree[/tex]
