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

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Answer 1 · 2017-12-09T12:32:12

See below.

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

$y = a sin (b x + c) + d$ $y=asin(bx+c)+d$

Where:

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

Period is $88 \frac{2 π}{b}$ $color(white)(88)(2pi)/b$

Phase shift is $88 \frac{- c}{b}$ $color(white)(88)(-c)/b$

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

$:.$

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 $y=sin(x) and y=sin(3x)$

enter image source here

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