What is the amplitude of the function f(x) = 1/2 cos(3x + π)

What is the amplitude of the function f(x) = 1/2 cos(3x + π) ?

  1. 1/3
  2. 1/2
  3. 3/2
  4. 2
  5. 3

Answer

The correct answer is B.

The amplitude of a function of the form g(x) = A cos(Bx + C) is |A|.

Alternatively,

-1 ≤ cos(3x + π) ≤ 1

-1/2 ≤ 1/2 cos(3x + π) ≤ 1/2.

The amplitude is then given by (maximum value - minimum value)/2

= [1/2 - (-1/2)]/2

= 1/2