Write an equation for a cosine function with an amplitude of 5, a period of 3, a phase shift of 2, and a vertical displacement of 2.

y = 5 cos 2π x-2/3 + 2

y = 3 cos π (x-2) - 5

y = 3 cos 2π (x-5) + 2

y = 5 cos 2π x+2/2 + 2

y = 5 cos ((2π/3)x - 2) + 2

Step-by-step explanation:

Cosine function takes a general form of  y = A cos (Bx + C) + D

Where

A is the amplitude

2π/B is the period

C is the phase shift ( if -C, then phase shift right, if +C phase shift left)

D is the vertical displacement (+D is above and -D is below)

Given the conditions of the function to build and the general form, we can write:

** Note: period needs to be 3, so 2π/B = 3, hence B = 2π/3

Now we can write:

y = 5 cos ((2π/3)x - 2) + 2

first answer choice is right.

x = 23.78

step-by-step explanation:

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