Cosine function

Question

a cosine function has an amplitude of 1/3, period of pi/3, horizontal shift of -2pi, and vertical shift of -3. 

What is the y-value of the negative function when x= pi? 

Answer 1

The form of the function is y = Acos(Bx+C) + D

 

  Amplitude = lAl = 1/3  Since you mention "negative function", I am assuming that you mean an inverted cosine graph.  So, A = -1/3.

 

  Period = 2π/B   2π/B = π/3  So, B = 6

 

  Horizontal shift = -C/B = -C/6 = -2π   So, C = 12π

 

  Vertical shift = D = -3

 

Therefore, y = (-1/3)cos[ 6x + 12π ] - 3

 

When x = π, y = (-1/3)cos(18π) - 3 = (-1/3)(1) - 3 = -10/3