Let's solve the problem step by step.
We are given that:
[tex]\[
\cos(x) = \frac{1}{3}
\][/tex]
We are asked to find [tex]\(\sin(90^\circ - x)\)[/tex].
To do this, we can use a fundamental trigonometric identity, specifically the co-function identity, which states:
[tex]\[
\sin(90^\circ - x) = \cos(x)
\][/tex]
Given this identity, we substitute the given value of [tex]\(\cos(x)\)[/tex]:
[tex]\[
\sin(90^\circ - x) = \frac{1}{3}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{\frac{1}{3}}
\][/tex]
