Question

Write a cosine function that has a midline of 4, an amplitude of 3 and a period of 8/5

Answer 1

A cosine function has the form

`y=A\cdot\cos (Bx+C)+D`

Where A is the amplitude, B is 2pi/T, and C is null in this case because the phase is not being specified, and D is the vertical shift (midline).

Using all the given information, we have

`y=3\cdot\cos ((2\pi)/(T)x)+4`

Then,

`y=3\cdot\cos ((2\pi)/((8)/(5))x)+4=3\cdot\cos ((10\pi)/(8)x)+4=3\cdot\cos ((5\pi)/(4)x)+4`

Hence, the function is

`y=3\cos ((5\pi)/(4)x)+4`