Solve for 0< x< 360, the equation sin(x+30)=-1/2

Below the explanation and result.

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

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