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##Mathematica, 60 bytes

NumberForm[t/.NSolve[Sin[t/180Pi]==#&&#2<=t<=#3,{t}],{9,3}]&

input

[0, -1080, 1080]

output

{-1080.000,-900.000,-720.000,-540.000,-360.000,-180.000,0.000,180.000,360.000,540.000,720.000,900.000,1080.000}

Mathematica, 60 bytes

NumberForm[t/.NSolve[Sin[t/180Pi]==#&&#2<=t<=#3,{t}],{9,3}]&

input

[0, -1080, 1080]

output

{-1080.000,-900.000,-720.000,-540.000,-360.000,-180.000,0.000,180.000,360.000,540.000,720.000,900.000,1080.000}

##Mathematica, 65 bytes

NumberForm[t/.NSolve[Sin[t Degree]==#&&#2<t<#3,{t},Reals],{9,3}]&

input

[0, -1080, 1080]

output

{-900.000,-720.000,-540.000,-360.000,-180.000,0.000,180.000,360.000,540.000,720.000,900.000}

##Mathematica, 60 bytes

NumberForm[t/.NSolve[Sin[t/180Pi]==#&&#2<=t<=#3,{t}],{9,3}]&

input

[0, -1080, 1080]

output

{-1080.000,-900.000,-720.000,-540.000,-360.000,-180.000,0.000,180.000,360.000,540.000,720.000,900.000,1080.000}

##Mathematica, 57 bytes

NumberForm[t/.NSolve[Sin@t==#&&#2<t<#3,{t},Reals],{9,3}]&

input

[0.5, 2, 10]

output

{2.618, 6.807, 8.901}

edit

3 decimal places fixed

##Mathematica, 65 bytes

NumberForm[t/.NSolve[Sin[t Degree]==#&&#2<t<#3,{t},Reals],{9,3}]&

input

[0, -1080, 1080]

output

{-900.000,-720.000,-540.000,-360.000,-180.000,0.000,180.000,360.000,540.000,720.000,900.000}