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
The cosine function should be [tex]f(x) = 5\times cos(5\times x) + 2[/tex]
A general cosine function is written as:
[tex]f(x) = A\times cos(\omega\times x) + M[/tex]
where
A is the amplitude
M is the midline
ω is the angular frequency.
Here, in the given situation
The amplitude is 5, then A = 5
The midline is 2, then M = 2
The period is [tex]2\times \pi\div 5[/tex]
The relation between the angular frequency ω and the period T is:
[tex]\omega = 2\times \pi\div T[/tex]
Now Then if the period is [tex]T = 2\div \pi\div 5,[/tex] replacing that in the above equation we find that:
[tex]\omega = 2\times \pi\div T = 2\times \pi\div (2\times \pi\div 5) = 5[/tex]
ω = 5
Then the function is [tex]f(x) = 5\times cos(5\times x) + 2[/tex]
Learn more: brainly.com/question/16911495
