Sure, let's solve the problem step-by-step:
Given: [tex]\(\cos (x) = \frac{1}{3}\)[/tex]
We need to find: [tex]\(\sin (90^\circ - x)\)[/tex]
First, recall the co-function identity for sine and cosine:
[tex]\[
\sin(90^\circ - x) = \cos(x)
\][/tex]
Using this identity:
[tex]\[
\sin(90^\circ - x) = \cos(x)
\][/tex]
We are given that:
[tex]\[
\cos(x) = \frac{1}{3}
\][/tex]
So, we can substitute this value to get:
[tex]\[
\sin(90^\circ - x) = \frac{1}{3}
\][/tex]
Thus, the value of [tex]\(\sin (90^\circ - x)\)[/tex] is [tex]\(\frac{1}{3}\)[/tex].
Therefore, the correct answer is:
[tex]\[
C. \frac{1}{3}
\][/tex]
