Question

How do you find the amplitude and period of `y= 2 - 3 cos pi•x`?

Answer 1

The amplitude is `=5`. The period is `=2`

Explanation:

The amplitude of `cosx` is

`-1<=cosx<=1`

Multiply by `-3`

`3>=-3cosx>=-3`

Add #2

`2+3>=(2-3cosx)>=2-3`

`5>=(2-3cosx)>=-1`

`-1<=(2-3cosx)<=5`

The period `T` of a periodic function `f(x)` is

`f(x)=f(x+T)`

Therefore,

`(2-3cospix)=2-3cospi(x+T)`

`=>`, `-3cos(pix)=-3cos(pix+piT)`

`=>`, `cos(pix)=cos(pix)cos(piT)-sin(pix)sin(piT)`

Comparing both sides of the equation

`{ (cospiT=1),(sinpiT=0):}`

`<=>`, `piT=2pi`

`=>`, `T=2`

The period is `=2`

graph{2-3cos(pix) [-10.03, 12.465, -2.81, 8.435]}