The sine function is periodic such that sinX=sin(X+2(pi)n) where n is an integer and the period is 2(pi). So sin(3t/2) is periodic when 3t2/2-3t1/2=2(pi)n, t2-t1=4/3(pi) (=2(pi)÷3/2), where t1 and t2 are two consecutive values of t separated by the period 4/3(pi). The amplitude is given by the coefficient 3/2*2=3 being the difference between the maximum and minimum values of sin, 1 and -1. 3t/2=(pi/2) and -(pi)t, so t=(pi)/3 and -(pi)/3. The range is between -3/2 and 3/2.