Question

Write a cosine function that has a midline of 3, an amplitude of 4 and a period
of pi.

Answer 1

`f(x)=4\cos(2x)+3`

Explanation:

Using the general equation
`f(x)=a\cos(bx+c)+d`, we already know that
`a=4` and
`d=3`, but we need to find
`b` from the period:

`(2\pi)/(|b|)=\pi\\ 2\pi=b\pi\\2=b`

Hence, the cosine function is
`f(x)=4\cos(2x)+3`