**Exploring
graphs of sine function**

by

**Behnaz
Rouhani**

In this assignment we will examine the graphs of

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.