Question

Write a cosine function that has a midline of 2, an amplitude of 4 and a period of 4/7

Answer 1

Answer:

$y= 4cos(\frac{7\pi }{2}x)+2$

Step-by-step explanation:

We know that the transformations of a cosine equation can be shown as:

y=±a(b(x-h))+k

Where 'a' is the amplitude

'b' is the horizontal change (Do 2π/b to find the period)

'h' is the horizontal shift

and 'k' is the vertical shift or midline.

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If the amplitude is 4, we can assume a=4.

Since the period is 4/7, we can solve for the 'b' value by:

$2\pi /\frac{4}{7}= \frac{7\pi }{2}$

Next, since the midline is 2, we know that a vertical shift of 2 occurred. Thus, the 'k' value is 2.

Writing this equation gives us:

$y= 4cos(\frac{7\pi }{2}x)+2$