Solving the trigonometric equations, the times at which the pendulum's movement will be 8 meters from its starting position are of:
[tex]x = 8\pi + 16n\pi[/tex] seconds.
What is the equation for the pendulum's position?
It is given by:
[tex]f(x) = -4\cos{\frac{x}{8}} + 4[/tex]
It is 8 meters from its starting position when f(x) = 8, hence:
[tex]f(x) = -4\cos{\frac{x}{8}} + 4[/tex]
[tex]8 = -4\cos{\frac{x}{8}} + 4[/tex]
[tex]4 = -4\cos{\frac{x}{8}}[/tex]
[tex]\cos{\frac{x}{8}} = -1[/tex]
We have that:
[tex]\cos{x} = -1 \rightarrow x = \pi + 2n\pi[/tex]
Hence:
[tex]\frac{x}{8} = \pi + 2n\pi[/tex]
[tex]x = 8\pi + 16n\pi[/tex] seconds.
More can be learned about trigonometric equations at https://brainly.com/question/24680641
