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NEED HELP ASAP!!!! Find an equation for the cosine graph

NEED HELP ASAP!!!! Find an equation for the cosine graph-example-1

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Answer:

y = 1 +cos(3/2(x+π/3))

Explanation:

You want the equation of a cosine graph.

Transformations

The usual transformations applied to a parent function are ...

  • a·f(x) — vertical expansion by a factor of 'a'
  • f(x-h) +k — translation by h units right and k units up
  • f(x/a) — horizontal expansion by a factor of 'a'

Vertical scale factor

The difference between the maximum and minimum of a cosine function is (1) -(-1) = 2. We observe that same difference on this graph, so there is no vertical scaling.

Translation

The maximum of a cosine function is found at (0, 1). On this graph, the nearest maximum is at (-π/3, 2). Subtracting the usual location gives the values of the horizontal and vertical translation:

(h, k) = (-π/3, 2) - (0, 1) = (-π/3, 1)

Horizontal scale factor

The period (from one peak to the next) of the graph is π -(-π/3) = 4π/3. The usual period of the cosine function is 2π, so this graph has been "expanded" by the factor (4π/3)/(2π) = 2/3.

Equation

Putting these transformations into the equation for the cosine function, we get ...

y = cos((x -(-π/3))/(2/3)) +1

y = 1 +cos(3/2(x +π/3)) . . . . equation of the graph

You can eliminate the inner parentheses by writing this in the equivalent form ...

y = 1 +cos(3/2x + π/2)

User Balaji Dhanasekar
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