Question

What is the equation of the graph below?

Answer 1

Answer:

y=cos(0.4x)

Step-by-step explanation:

Answer 2

Answer:

The equation of the graph given is:

                  $y=\cos(0.4x)$

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:

$y=cos(bx)$ is given by:

$Period=\dfrac{2\pi}{5}$

1)

$y=\cos(\dfrac{x}{0.4})$

The period of this function is:

$Period=\dfrac{2\pi}{\dfrac{1}{0.4}}\\\\\\Period=0.8\pi\neq 5\pi$

Hence, option: 1 is incorrect.

2)

$y=\cos (5x)$

The period of this function is:

$Period=\dfrac{2\pi}{5}\\\\\\Period=\dfrac{2}{5}\pi\neq 5\pi$

Hence, option: 2 is incorrect.

4)

$y=\cos (\dfrac{x}{5})$

The period of this function is:

$Period=\dfrac{2\pi}{\dfrac{1}{5}}\\\\\\Period=10\pi\neq 5\pi$

Hence, option: 4 is incorrect.

3)

$y=\cos(0.4x)$

The period of this function is:

$Period=\dfrac{2\pi}{0.4}\\\\\\Period=5\pi$

        Hence, option: 3 is the correct option.