Question

PLEASE HELP 20+ POINTS!! What is the cosine equation of the function shown?

Answer 1

Answer:   $\bold{y=7\ \cos\bigg(x-\dfrac{\pi}{4}\bigg)-4}$

Step-by-step explanation:

y = A cos (Bx - C) + D

• A (amplitude) = max - D
• B = Period/2π  --->   Period is the distance from max to next max
• C = B · Phase Shift  ---> Phase shift is distance from y-axis to max
• D (vertical shift) = (max + min)/2

D = (max + min)/2     =     (3 - 11)/3      =  -4

A = max - D               =     3 - (-4)         = 7

Period = 9π/4 - π/4   =    8π/4            = 2π

B = Period/2π           =    2π/2π          = 1

Phase Shift = π/4 - 0 =     π/4

C = B · Phase Shift    =  1 · π/4            = π/4

Equation:

           y = 7 cos (1·x - π/4) + (-4)