How do you use transformation to graph the sin function and determine the amplitude and period of #y=sin(3x)#?

1 Answer
Dec 9, 2017

Answer:

See below.

Explanation:

We can find the transformation of #sin(x)# to #sin(3x)# using the following equation:

#y=asin(bx+c)+d#

Where:

Amplitude is #color(white)(88)a#

Period is #color(white)(88)(2pi)/b#

Phase shift is #color(white)(88)(-c)/b#

Vertical shift is #color(white)(88)d#

#:.#

For #color(white)(88)y=sin(3x)#

Amplitude is 1, (This is the same as #sin(x)#)

Period is #color(white)(88)(2pi)/b=(2pi)/3# ( period of #sin(x)# is #2pi#)

( This is a compression in the horizontal direction by a factor of 3 )

Phase shift is #color(white)(88)(-c)/b=0/3=0# ( No phase shift )

Vertical shift is #color(white)(88)d=0# ( No vertical shift )

Graph of #y=sin(x) and y=sin(3x)#

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