Question

Write the equation of a sine or cosine function to describe the graph.

Answer 1

Answer:

  y = cos(3/2x)

Step-by-step explanation:

A general sine or cosine function will have parameters of amplitude, vertical and horizontal offset, and period. The values of these parameters can be determined from the given graph.

  y = A·cos(2π(x -B)/P) +C

where A is the amplitude, B and C are the horizontal and vertical offsets, and P is the period.

Amplitude

For sine and cosine functions, the amplitude of the function is half the difference between the maximum and minimum:

  A = (3 -1)/2 = 1

Horizontal offset

A sine function has its first rising zero-crossing at x=0. A cosine has its first peak at x=0. The given graph has its first peak at x=0, so it is a cosine function with no horizontal offset.

  B = 0

Vertical offset

For sine and cosine functions, the vertical offset is the average of the maximum and minimum values:

  C = (3 +1)/2 = 2

Period

The period is the difference in x-values between points where the function starts to repeat itself. Here, we can use the peaks to identify the period as 4π/3.

  P = 4π/3

Function equation

Using the parameter values we determined, the function can be written as ...

  y = cos(3/2x) +2

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Additional comment

The argument of the cosine function is ...

  $\dfrac{2\pi(x-B)}{P}=\dfrac{2\pi(x-0)}{\dfrac{4\pi}{3}}=\dfrac{3(2\pi)}{4\pi}x=\dfrac{3}{2}x$