Question

If x represents time measured in seconds since the ride first began, at what times will the pendulum's movement be 4 meters from its starting position?

Answer 1

Given

The function

`f(x)=-2\cos (x)/(4)+2`

To find the time at which the pendulum is 4 meters away from its starting point.

Now,

Let x be the time at which the pendulum moves.

Let f(x) be the distance of the pendulum from its starting point at time x.

Then,

`f(x)=4(\text{Given)}`

Therefore,

`\begin{gathered} 4=-2\cos (x)/(4)+2 \\ -2\cos (x)/(4)=4-2 \\ -2\cos (x)/(4)=2 \\ -\cos (x)/(4)=1 \end{gathered}`

Since

`\sin (n\pi-\theta)=-\cos \theta`

Then,

`\begin{gathered} \sin (n\pi-(x)/(4))=1 \\ n\pi-(x)/(4)=-(\pi)/(2) \\ n\pi-(x)/(4)=-(\pi)/(2) \\ (x)/(4)=n\pi+(\pi)/(2) \\ x=4n\pi+\pi \end{gathered}`

Hence, the answer is option c).