Question

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

Answer 1

Answer:

$3\cos(\frac{8\pi}{5}x)+5$

Step-by-step explanation:

Recall that a cosine function of the form $A\cos(Bx-C)+D$ has the following:

- amplitude A

- Frequeny $\frac{B}{2\pi}$.

- Phase shift $\frac{C}{B}$

- Midline D

So, in our case, we know that A=3, $\frac{B}{2\pi}=\frac{4}{5}$(which implies that $B=\frac{8\pi}{5}$) and D=5. Since we are not said everything about the Phase shift, lets asumme that the Phase shift is 0. Hence C=0.

Then, our desired function is $3\cos(\frac{8\pi}{5}x)+5$