Question

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

Answer 1

Answer:

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

Step-by-step 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:

$\frac{2\pi}{|b|}=\pi\\ 2\pi=b\pi\\2=b$

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