Question

If csc θ = 5 , what is the measure of the angle θ?

Answer 1

csc θ = 5

so
1 / sin θ = 5
so
sin θ = 1/5
so
θ = 11.54 degrees

Answer 2

Or....

since sin θ = +1/5, θ could be in quadrants I or II
θ = 11.54· or 168.46°