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

Question

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

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Answer 1 · 2017-12-11T21:39:15

See below.

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#