Question

State the amplitude and period of f(x)= 3cos 9/5 (t)

Answer 1

The period is
`(10\pi)/(9)` and the amplitude is 3.

Explanation:

The period goes from one peak to the next (or from any point to the next matching point). The amplitude is the height from the center line to the peak.

The period of the function
`y=a\cos (bx)` is
`T=(2\pi )/(b)` and the amplitude is
`|a|.`

Consider the function
`f(t)=3\cos \left((9)/(5)t\right).`

The period for the function
`f(t)` is

`T=(2\pi)/((9)/(5))=(2\pi)/(1)\cdot (5)/(9)=(10\pi)/(9)`

and the amplitude is 3.