Answer:
The equation of the graph given is:
[tex]y=\cos(0.4x)[/tex]
Step-by-step explanation:
Clearly from the graph of the function that is provided to us we see that the graph repeats itself after every 5π.
i.e. the period of the function is: 5π.
Now we will check in each of the given options whose period is 5π.
We know that the period of a cosine function of the type:
[tex]y=cos(bx)[/tex] is given by:
[tex]Period=\dfrac{2\pi}{5}[/tex]
1)
[tex]y=\cos(\dfrac{x}{0.4})[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{\dfrac{1}{0.4}}\\\\\\Period=0.8\pi\neq 5\pi[/tex]
Hence, option: 1 is incorrect.
2)
[tex]y=\cos (5x)[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{5}\\\\\\Period=\dfrac{2}{5}\pi\neq 5\pi[/tex]
Hence, option: 2 is incorrect.
4)
[tex]y=\cos (\dfrac{x}{5})[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{\dfrac{1}{5}}\\\\\\Period=10\pi\neq 5\pi[/tex]
Hence, option: 4 is incorrect.
3)
[tex]y=\cos(0.4x)[/tex]
The period of this function is:
[tex]Period=\dfrac{2\pi}{0.4}\\\\\\Period=5\pi[/tex]
Hence, option: 3 is the correct option.
