Question

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

Answer 1

Explanation

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

Where A is the Amplitude =5

Also

$\begin{gathered} period=\frac{2\pi}{B} \\ 4=\frac{2\pi}{B} \\ 4B=2\pi \\ B=\frac{2\pi}{4} \\ B=\frac{\pi}{2} \end{gathered}$

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

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

Answer:

$y=5cos(\frac{\pi}{2}x)+3$