The right answer is:
"Yo trabajo en mi tarea".
That´s because is talking in first person.
"Trabajas" is for "you".
"Trabajan is for "they"
and "Trabajamos" is for "we"
esta would be the right way to say it
Try this:
Saludos,
No vas a creer él trabajo que tuve que hacer la semana pasada. ¡Mi mama me hico limpiar le casa entera! Primero, tenia que fregar una montaña de platos. Tambien tenia que sacar la basura. Despues, me hico limpiar el baño. ¡Que asco! Tenia que barrer el piso de la cass entera. Tambien corte la grama. Finalmente, después que termine pasando la aspiradora y planchando la ropa, pude descansar. ¿Y tu que hiciste la semana pasada?
Sinceramente,
[Tu nombre]
Translation:
Salutations,
You won't believe the amount of work I had to do last week. My mom made me clean the entire house! First, I washed a mountain of dishes. I also had to take out the trash. Then, I had to clean the bathroom. How disgusting! I had to sweep the floor of the entire house. I also cut the grass. Finally, after I finished vacuuming and ironing the clothes, I was able to rest. What did you do last week?
Sincerely,
[Your Name]
Answer:
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