Answer:
Below the explanation and result.
Step-by-step explanation:
1) divide in possible cases
sin(x+30)=1/2
2) isolate "x + 30" and simplify
sin(x+30)=1/2
sin (π-(x+30))=1/2
3) calculate and isolate π-x-30
x+30= arcsin (-1/2)
sin (π-x-30)=-1/2
4)add period and calculate
x+30= -(π/6)
π-x-30=arcsin(-1/2)
5) resolve the equation and add the period
x+30= -π/6 +2kπ, k∈Z
π - x - 30= -π/6
6) resolve the equation
x= -π/6 - 30 + 2kπ, k∈Z
π-x-30=π/6+2kπ,k∈Z
7) like -2kπ=2kπ, so k∈Z
x=-π/6-30+2kπ,k∈Z
x=7π/6-30-2kπ,k∈Z
8) Find the union
x=-π/6-30+2kπ,k∈Z
x=7π/6-30+2kπ,k∈Z
9) RESULT:
x=-30+7π/6+2kπ,k∈Z
x=-30+11π/6+2kπ,k∈Z