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Write a cosine function that has an amplitude of 2, a midline of 5 and a period of 8.

Sagot :

Answer:

y=2 cos (π/4x-π/4)

Step-by-step explanation:

Given

A cosine function has an amplitude of 2, a midline of 5 and a period of 8.

To find:

A cosine function.

Explanation:

Let the function be,

[tex]y=Acos(ws+p)[/tex]

Since amplitude is 2.

Then,

[tex]A=2[/tex]

Also, since the period is 8.

Then,

[tex]w=\frac{2\pi }{8}[/tex]

[tex]w=\frac{\pi }{4}[/tex]

And, since midline is 5.

Hence, the cosine function is,

y=2 cos ([tex]\frac{\pi }{4}[/tex]x-[tex]\frac{\pi }{4}[/tex]

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