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Write a sine function that has an amplitude of 5, a midline of 4 and a period of 3/2

Sagot :

Note that in any sine function :

[tex]y=A\sin (B(x+C))+D[/tex]

Amplitude = A

Verical Shift or midline = D

Period = (2π)/B

Horizontal or Phase Shift = C

From the given,

since we dont have any horizontal shift, C = 0.

Amplitude = 5, so A = 5

Midline = 4, so D = 4

and

Period = 3/2, so equating it to (2 π)/B

[tex]\frac{3}{2}=\frac{2\pi}{B}[/tex][tex]B=\frac{4\pi}{3}[/tex]

Now, substituting the values obtained, the sine function will be :

[tex]y=5\sin (\frac{4\pi}{3}x)+4[/tex]

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