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


Enter your answer by filling in the boxes. Enter any phase shift as its smallest multiple from the fundamental period.

PLEASE HELP 20+ POINTS!! What is the cosine equation of the function shown?Enter your answer by filling in the boxes. Enter any phase shift as its smallest mult class=

Answer :

tramserran

Answer:   [tex]\bold{y=7\ \cos\bigg(x-\dfrac{\pi}{4}\bigg)-4}[/tex]

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)

               

The cosine equation of the function should be [tex]y = 7\cos (x - \frac{\pi}{4}) - 4[/tex]

Calculation of cosine equaton:

Since

y = A cos (Bx - C) + D

A (amplitude) = max - D

B = Period/2[tex]\pi[/tex]  =   Period represent the distance from max to next max

C = B · Phase Shift = Phase shift is distance from y-axis to max

D (vertical shift) =[tex](max + min)\div 2[/tex]

So,

D  [tex]= (max + min)\div 2 = (3 - 11)\div 3[/tex]     =  -4

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

Period = [tex]9\pi \div 4 - \pi \div 4 = 8\pi \div 4 = 2\pi[/tex]

B = [tex]Period\div 2\pi = 2\pi\div 2\pi[/tex]     = 1

Phase Shift = [tex]\pi \div 4 - 0 = \pi \div 4[/tex]

C = B · Phase Shift    =  [tex]1. \pi \div 4 = \pi \div 4[/tex]

So, the above equation should be considered.

Learn more about cosine here: https://brainly.com/question/16299322

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