[inputrad]plot( 1/2*sin(x/3 - pi), x=0..20)[/inputrad]
1/2*sin(x/3 - pi)
you can ignore - pi for period considerations, because this only moves the graph.
1/2*sin(x/3)
1/2* can be ignored, because it only "scales" the graph (height).
so analyze:
sin(x/3)
every value of x is divided by 3, so the period has to be 3 times the period of sin(x).
sin(x) has a period of 360deg = 2*Pi. So sin(x/3) has a period of 3*2*Pi = 6*Pi ≈ 18.84955592153876
+3146 
