Question

What is the amplitude of y=1/2 sin2x

Answer 1

$(-\frac{1}{2},\frac{1}{2})$
Amplitutde:
$(\frac{1}{2}-(-\frac{1}{2}))=1$
Normally for sinx amplitude is 2 (1 +1). In the case when it is half sine amplitude is halved, therefore 0.5 +0.5 = 1 Paramers alpha = 2x does not matter because it only stretches the graph horizontally.

Answer 2

$for\ each\ \alpha \in R\ \ \ \ (for\ example\ \alpha =2x) \\\\the\ max\ of\ y=sin \alpha \ is\ 1\ \ \ and\ \ \ the\ min\ of\ y=sin \alpha \ is\ -1\\\\ the\ amplitude\ of \ \ \ \ y=sin \alpha \ \ \ \ is\ \ \ \ 1-(-1)=2\\\\\\then\ the\ amplitude\ of \ \ \ \ y= \frac{1}{2} sin 2x \ \ \ \ is\ \ \ \ \frac{1}{2} \cdot2= 1$