Assignment 1

Exploring graphs of sine function

by

Behnaz Rouhani

In this assignment we will examine the graphs of
y = a sin (bx + c)
for different values of a, b, and c.

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.

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