2 Answers

Poras Bhardwaj · Answer 1 · 2020-10-16T02:27:37+0000

Answer:

The equation of the graph given is:

$y=\cos(0.4x)$

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:

$Period=(2\pi)/(5)$

1)

$y=\cos((x)/(0.4))$

The period of this function is:

$Period=(2\pi)/((1)/(0.4))\\\\\\Period=0.8\pi\\eq 5\pi$

Hence, option: 1 is incorrect.

2)

$y=\cos (5x)$

The period of this function is:

$Period=(2\pi)/(5)\\\\\\Period=(2)/(5)\pi\\eq 5\pi$

Hence, option: 2 is incorrect.

4)

$y=\cos ((x)/(5))$

The period of this function is:

$Period=(2\pi)/((1)/(5))\\\\\\Period=10\pi\\eq 5\pi$

Hence, option: 4 is incorrect.

3)

$y=\cos(0.4x)$

The period of this function is:

$Period=(2\pi)/(0.4)\\\\\\Period=5\pi$

Hence, option: 3 is the correct option.

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