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

1 Answer
Dec 11, 2017

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