Question

Write a cosine function that has an amplitude of 5, a midline of 2 and a period of \frac{2\pi}{5} 5 2π ​ .

Answer 1

Answer:

f(x) = 5*cos(5*x) + 2

Step-by-step explanation:

A general cosine function is written as:

f(x) = A*cos(ω*x) + M

where:

A is the amplitude

M is the midline

ω is the angular frequency.

In this case we know that:

The amplitude is 5, then A = 5

The midline is 2, then M = 2

The period is 2*pi/5

The relation between the angular frequency ω and the period T is:

ω = 2*pi/T

Then if the period is T = 2*pi/5, replacing that in the above equation we find that:

ω = 2*pi/T = 2*pi/(2*pi/5) = 5

ω = 5

Then the function is:

f(x) = 5*cos(5*x) + 2