What is the amplitude of #y=-2/3sinx# and how does the graph relate to #y=sinx#?

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Answer 1 · 2018-02-11T16:27:19

See below.

We can express this in the form:

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

Where:

From our example:

#y=-2/3sin(x)#

We can see the amplitude is #bb(2/3)#, amplitude is always expressed as an absolute value. i.e.

#|-2/3|=2/3#

#bb(y=2/3sinx)# is #bb(y=sinx)# compressed by a factor of #2/3# in the y direction.

#bb(y=-sinx)# is #bb(y=sinx)# reflected in the x axis.

So:

#bb(y=-2/3sinx)# is #bb(y=sinx)# compressed by a factor #2/3#in the direction of the y axis and reflected in the x axis.

Graphs of the different stages:

enter image source here