Question

What is the period and amplitude for `y=cos9x`?

Answer 1

The period is `=2/9pi` and the amplitude is `=1`

Explanation:

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

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

Here,

`f(x)=cos9x`

Therefore,

`f(x+T)=cos9(x+T)`

`=cos(9x+9T)`

`=cos9xcos9T+sin9xsin9T`

Comparing `f(x)` and `f(x+T)`

`{(cos9T=1),(sin9tT=0):}`

`=>`, `9T=2pi`

`=>`, `T=(2pi)/9`

The amplitude is `=1` as

`-1<=cosx<=1`

graph{cos(9x) [-1.914, 3.56, -0.897, 1.84]}