Answer:
y = -3 cos 5x
Step-by-step explanation:
First, let's start by defining the standard form of a cosine function:
[tex]y(x)=Acos(\omega x)[/tex]
Where:
[tex]A=Amplitude\\\omega= Angular\hspace{3}frequency[/tex]
The angular frequency is:
[tex]\omega= 2\pi f[/tex]
So:
[tex]f=\frac{\omega}{2 \pi}[/tex]
Frequency is a quantity that measures the number of repetitions per unit of time of any phenomenon or periodic event. In other words, for the cosine function, it is the number of cycles during its period of oscillation.
From one of the equations provided:
[tex]y=-3cos(5x)[/tex]
You can extract the angular frequency, so:
[tex]f=\frac{5}{2 \pi}[/tex]
This tells you that the number of cycles during the period of oscillation (which is 2π) is 5. As you can see from the graph provided, the number of cycles of the function is 5.
Now, why -3. Well, as you may know, for x=0:
[tex]y(0)=cos(0)=1[/tex]
Thus, for x=0, this functions is always equal to 1. But from the graph you may note that the function for x=0 is equal to -3, hence,
[tex]A=-3\\\\Because:\\\\y(0)=-3 *cos(0)=-3*(1)=-3[/tex]
Therefore the answer is:
[tex]y=-3cos(5x)[/tex]
I attached you the graph, so you can corroborate the answer.
