SOLUTION: For what numbers <font face = "symbol">q</font>, 0&#8806;<font face = "symbol">q</font>&#8806;2<font face = "symbol">p</font> does cos<font face = "symbol">q</font> = 1? Can you

On the unit circle, each point is (cos(q),sin(q)), where q is the angle between 
the right hand side of the x-axis and the radius drawn to that
point:



So you want to know where cosq = 1.

Since the x-coordinate of every point on the unit circle IS the
cosine of the angle that the radius to that point makes with
the right side of the x-axis, we are looking for a point on that
circle with an x-coordinate of 1.  There is only one point on
the unit circle that has its x-coordinate as 1, and that is the
point (1,0)



and the value of q there is either 0 or 2p.  

So that's the answer.  q = 0 or 2p.
 
Edwin