Exploring graphs of sine function
First we are going to see the effect of changing a in y = a sinx. Amplitude of the sine function is absolute value of a. Graphs with thin lines are graphs of
y = sinx blue
y = 2sinx green
y = 3sinx red
with amplitudes of 1, 2, and 3 respectively. Graphs with solid lines are graphs of
y = -sinx blue
y = -2sinx green
y = -3sinx red
Graph of y = sin2x goes through the origin with period of pi, and this is the graph represented in green. Graph of y = sin(2x+4) [blue graph] is the horizontal translation of the graph of y = sin2x by two units to the right. This could also be explained by saying that, in this case we have a phase shift, and to determine the phase shift we would set the parentheses equal to zero and solve for x. Doing this would yield x = -2, which in turn would shift the graph 2 units to the left.
Graph of y = sin(2x-4) [red
graph] is the graph of y = sin2x translated 2 units to the right
as its phase shift is x = 2.