# How do you find the amplitude and period of y = -2 sin (1/2) x?

Amplitude is $2$ and period is $4 \pi$
For a general sine graph of form $y = a \sin b x$, the amplitude is $| a |$ and the period is $\frac{2 \pi}{b}$
So in this case the amplitude is $2$ and the period is $\frac{2 \pi}{1 / 2} = 4 \pi$
This means that the maximum displacement from the rest position or x axis is 2 units, and the time taken for 1 complete cycle on the x-axis is $4 \pi$ radians.