Question

At an amusement park, the pendulum ride's movement from its starting position in meters can be represented by the equation f of x is equal to negative 4 times the cosine of the quantity x over 8 end quantity plus 4 period If x represents time measured in seconds since the ride first began, at what times will the pendulum's movement be 8 meters from its starting position?

Answer 1

Given

`f(x)=-4\cos((x)/(8))+4`

To find x when f(x)=8.

Step-by-step explanation:

It is given that,

`f(x)=-4\cos((x)/(8))+4`

Then, for f(x)=8,

`\begin{gathered} 8=-4\cos\mleft((x)/(8)\mright)+4 \\ 4\cos((x)/(8))=-4 \\ \cos((x)/(8))=-1 \\ (x)/(8)=(2n+1)\pi \\ x=8\pi(2n+1) \\ x=(8\pi+16n\pi)sec \end{gathered}`

Hence, the answer is

`x=(8\pi+16n\pi)sec`