Question

What is the amplitude of the function:
f(x) = 1/2cos(3x+π) ?
The answer is 1/2, but I don't know why.

Answer 1

Because that is the number in front of cosine or sine. Also because from the midline the function goes up and down 1/2 units.

Answer 2

Also known as a vertical stretch

Answer 3

here is a graph of
cos x
2 cos x
3 cosx

you can see the amplitude or vertical stretch

Answer 4

Hint:
It's not a bad idea to learn the definition of terms about periodic functions here:
https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html

Answer 5

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