Given
The function
[tex]f(x)=-2\cos \frac{x}{4}+2[/tex]
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,
[tex]f(x)=4(\text{Given)}[/tex]
Therefore,
[tex]\begin{gathered} 4=-2\cos \frac{x}{4}+2 \\ -2\cos \frac{x}{4}=4-2 \\ -2\cos \frac{x}{4}=2 \\ -\cos \frac{x}{4}=1 \end{gathered}[/tex]
Since
[tex]\sin (n\pi-\theta)=-\cos \theta[/tex]
Then,
[tex]\begin{gathered} \sin (n\pi-\frac{x}{4})=1 \\ n\pi-\frac{x}{4}=-\frac{\pi}{2} \\ n\pi-\frac{x}{4}=-\frac{\pi}{2} \\ \frac{x}{4}=n\pi+\frac{\pi}{2} \\ x=4n\pi+\pi \end{gathered}[/tex]
Hence, the answer is option c).
