I will first reveal the most obvious secret of trig: Most of the problems are 30/60/90 or 45/45/90 triangles of some sort.
The rule to remember is
has solutions
integer 
Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is
.
integer
In the range we want, that's
with the plus sign and 
with the minus, so
or 
or 
The rule to remember is
Continuing where we left off, a cosine of -1/2 is a 30/60/90 triangle in the second or third quadrant; we pick second, and a little thought tells us the angle is
In the range we want, that's
