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MathPhys

Answer:

y = 4 sin(2π/11 x) + 2

Step-by-step explanation:

y = A sin(2π/T x + B) + C

where A is the amplitude,

T is the period,

B is the phase shift,

and C is the midline.

A = 4, T = 11, and C = 2.  We'll assume B = 0.

y = 4 sin(2π/11 x) + 2

The sine function with the desired characteristics is given by:

[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]

The standard sine function is given by:

[tex]y = A\sin{Bx} + C[/tex]

  • The amplitude is 2A.
  • The period is [tex]\frac{2\pi}{B}[/tex].
  • The midline is C.

In this problem:

  • Midline of 2, thus [tex]C = 2[/tex].
  • Amplitude of 4, thus [tex]2A = 4 \rightarrow A = 2[/tex].
  • Period of 11, thus [tex]\frac{2\pi}{B} = 11 \rightarrow B = \frac{2\pi}{11}[/tex]

Then, the equation for the sine function is:

[tex]y = 2\sin{\left(\frac{2\pi}{11}\right)} + 2[/tex]

A similar problem is given at https://brainly.com/question/18055768

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