Question

Find the amplitude of the function `2y=cos (4(t-6))+6`?

I know that the simplified form is y=cos(4(t-6))+3
The textbook says that the amplitude is `1/2` but I don't know how to get to the answer

Answer 1

See below.

Explanation:

When a trigonometric function is arranged in this form:

`y =acos(bx +c )+d`

The amplitude is a

The period is `(2pi)/b`

Phase shift is `-c/b`

Vertical shift is `d`

First rearrange `2y=cos(4(t-6))+6`

Multiply by `1/2`

`y=1/2cos(4(t-6))+3`

Since `a=1/2`

The amplitude is `1/2`