What happens when the a (amplitude) of a sine graph is negative #-2 sin (1/4 x)#?

1 Answer
Gió
Apr 29, 2015

It simply flips your graph upsidedown. Where it should have a positive amplitude, now gets negative and viceversa:
For example:
if you choose #x=pi# yo get #sin(pi/4)=sqrt(2)/2# but with minus 2 in front your amplitude becomes: #-2sqrt(2)/2=-sqrt(2)#:
Graphically you can see this comparing:
#y=2sin(x/4)#
graph{2sin(x/4) [-11.25, 11.25, -5.625, 5.625]}
with:
#y=-2sin(x/4)#
graph{-2sin(x/4) [-12.66, 12.65, -6.33, 6.33]}

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