Question

Find the cosine function that is represented in the graph.

Answer 1

Answer:

f(x)=4cos(5x)

Step-by-step explanation:

Let us see the standard form of cosine function

f(x) = acos(nx)

Where x is the angle in radians along x axis

for x=0 , we see that the value of f(x) = 4

Hence acos(n*0)=4

           acos 0 = 4

           a *1 = 4    (as cos 0 = 1)

Hence we have a = 4 , therefore our equation becomes

f(x) = 4 cos (nx)

from the given graph we can see that

for x = $\frac{\pi }{5}$   f(x) = -4

Hence

$4cos(\frac{n\pi}{5}) = -4$

dividing both sides by 4 we get

$cos(\frac{n\pi}{5} )=-1\\cos(\frac{n\pi}{5})=cos \pi\\Hence \\\frac{n\pi}{5}=\pi\\n\pi= 5\pi\\n=5$

Hence we have value of n also as 5

Hence our function is

f(x) = $4cos(5x)$