Question

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

Answer 1

Step-by-step explanation

`y=Acos(Bx+C)+D`

Where A is the Amplitude =5

Also

`\begin{gathered} period=(2\pi)/(B) \\ 4=(2\pi)/(B) \\ 4B=2\pi \\ B=(2\pi)/(4) \\ B=(\pi)/(2) \end{gathered}`

D represents the midline. While C is the phase shift that is not given, Therefore, the equation becomes;

`\begin{gathered} y=5cos((\pi)/(2)x+0)+3 \\ y=5cos((\pi)/(2)x)+3 \end{gathered}`

Answer:

`y=5cos((\pi)/(2)x)+3`