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

1 Answer
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 $\sin \left(\frac{\pi}{4}\right) = \frac{\sqrt{2}}{2}$ but with minus 2 in front your amplitude becomes: $- 2 \frac{\sqrt{2}}{2} = - \sqrt{2}$:
Graphically you can see this comparing:
$y = 2 \sin \left(\frac{x}{4}\right)$
graph{2sin(x/4) [-11.25, 11.25, -5.625, 5.625]}
with:
$y = - 2 \sin \left(\frac{x}{4}\right)$
graph{-2sin(x/4) [-12.66, 12.65, -6.33, 6.33]}