Graph two cycles of each of the following. State the domain and range of the cycle.

Question

a) 2sin ((1/2)θ)

b) -3cos((1/2)θ - 90) +1

Answer 1

a) is a standard sine wave stretched vertically by a factor of 2, so now the amplitude is twice as large and the max and min values are 2 and -2 instead of 1 and -1. then the period is doubled due to the 1/2 before the angle. sinoid function is AsinB(x+C)+D C and D are just zero, but A doubled and B was halved. B =2pi/period. for B=1 the period is 2pi. for B=1/2 the period doubles to 4pi

2 cycles would mean from x= 0 to 8pi