Answer:
[tex]y= 4cos(\frac{7\pi }{2}x)+2[/tex]
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.
------------------------------------------------------
If the amplitude is 4, we can assume a=4.
Since the period is 4/7, we can solve for the 'b' value by:
[tex]2\pi /\frac{4}{7}= \frac{7\pi }{2}[/tex]
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:
[tex]y= 4cos(\frac{7\pi }{2}x)+2[/tex]
