Question

Find the cosine function that is represented in the graph.

Answer 1

f(x)=4cos(5x)

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 =
`(\pi )/(5)` f(x) = -4

Hence

`4cos((n\pi)/(5)) = -4`

dividing both sides by 4 we get

`cos((n\pi)/(5) )=-1\\cos((n\pi)/(5))=cos \pi\\Hence \\(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)`