​ trig

$2sin(3x+45^\circ)=1\\ sin(3x+45^\circ)=\frac{1}{2}\\ 3x+45^\circ=(30+360n)^\circ\quad or \quad (150+360n)^\circ\\ 3x+45^\circ=[180n+(-1)^n*30] ^\circ\\ 3x^\circ=[180n-45+(-1)^n*30] ^\circ\\ x^\circ=[60n-15+(-1)^n*10] ^\circ\\ x=60n-15+10(-1)^n\\ $

n is in the set of integers.

That needs to be carefully checked.

b)     What is closest to 200degrees?        x  or    3x+45  ?   

         I don't understand what is being asked here.