Question

What are the amplitude, period, and phase shift of the given function? f(t)=-2/3 cos (3t-3pi)

Answer 1

amplitude;
`(2)/(3)`

Phase shift;
`\pi` units right

Period;
`(2\pi)/(3)`

Explanation:

The given function is

`y=-(2)/(3)\cos(3t-3\pi)`

This function is of the form;

`y=A\sin (Bt+C)`

The period is given by:

`|A|=|-(2)/(3)|= (2)/(3)`

The period is given by:

`T=(2\pi)/(|B|)= (2\pi)/(|3|)=(2\pi)/(3)`

The phase shift is given by;

`(C)/(B)=(-\3pi)/(3)=- \pi` or
`\pi` units right.