Question

a). What is the period?
b). What is the amplitude?
c). How is the graph related to its parent graph y = sinx or y = cosx?

y=3cos(x/2) and y=2sin(2pix)+1

Answer 1

sin x and cos x are both periodic with period 2pi. i.e., for sin x, sin x = sin (x + 2pi) for any x.

So then, you want to find the period p: cos (x / 2) = cos( (x+p) / 2 ) = cos( x/2 + p/2 ) if p/2 = 2 pi. i.e. p=4pi.

Answer 2

I know the period for the first equation is 4pi and amplitude is 3 but how does it relate to y=cosx?

Answer 3

well cos x has amplitude 1, and period 2pi. so does sin x. So these new functions are the same, but stretched somehow in the vertical and horizontal direction. If you think about it, that's what amplitude and period, in comparison the sin and cos, mean here.

Answer 4

they stretched.

Answer 5

by how much? That's what they want you to say. "new function is like cos x but stretched by ___ vertically, and ___ horizontally". (or sin function...)

Answer 6

stretched by 3 vertically and 1/2 horizonatally?