Answer:
[tex]t=0.0107\ \text{s}[/tex]
Explanation:
[tex]x=10\cos(6t)[/tex]
Now [tex]x=8\ \text{cm}[/tex]
Substituting the value of [tex]x[/tex] in the equation we get
[tex]8=10\cos6t[/tex]
[tex]\Rightarrow 0.8=\cos6t[/tex]
[tex]\Rightarrow \cos^{-1}0.8=6t[/tex]
[tex]\Rightarrow t=\dfrac{\cos^{-1}0.8}{6}[/tex] the values here are used found in radians
[tex]\Rightarrow t=0.0107\ \text{s}[/tex]
So, at [tex]t=0.0107\ \text{s}[/tex] the value of [tex]x=8\ \text{cm}[/tex].
