To determine the value of [tex]\(3x\)[/tex] using an appropriate inverse trigonometric expression, we start with the given equation:
[tex]\[
\cos(3x) = -1
\][/tex]
We need to find the angle for which the cosine is [tex]\(-1\)[/tex]. In the unit circle, the angle where the cosine equals [tex]\(-1\)[/tex] is [tex]\( \pi \)[/tex] (180 degrees), plus any multiple of [tex]\(2\pi\)[/tex] (360 degrees), since cosine is periodic with a period of [tex]\(2\pi\)[/tex].
Therefore, the general solution for [tex]\(3x\)[/tex] can be written as:
[tex]\[
3x = \pi + 2n\pi
\][/tex]
where [tex]\(n\)[/tex] is any integer. This equation defines the set of all angles [tex]\(3x\)[/tex] that satisfy the original equation.
