Question

y=2cos(1/2x) Find amplitude and the period. And can you show me a rough sketch of how the graph would look. I know the amp. is 2

Answer 1

Since you're doing this, I assume you've done functional notation and know the basic functions. So, this is similar to how you would go about graphing it (transforming functions). \[y = a \cos(b(x-h \pi))+k\]

So say we have to sketch, \[y=-1/3 \cos \theta +2/3\]
Start off with the vertical displacement -> use the amplitude to determine where the MAX and MIN lines are -> See whether it's positive or negative.

notice amplitude is -1/3, period is 2 pi, vertical displacement 2/3, domain is all real numbers and range is 1/3<=y<=1 So this will help you visualize what everything is.