To solve the problem, we need to determine the value of [tex]\( x \)[/tex] given that [tex]\(\cos x = \sin 16^\circ\)[/tex].
We start with the identity involving sine and cosine functions:
[tex]\[ \sin \theta = \cos (90^\circ - \theta) \][/tex]
This means that for any angle [tex]\( \theta \)[/tex], the sine of [tex]\( \theta \)[/tex] is equal to the cosine of [tex]\( 90^\circ - \theta \)[/tex].
Given the problem:
[tex]\[ \cos x = \sin 16^\circ \][/tex]
Using the identity, we can write:
[tex]\[ \sin 16^\circ = \cos (90^\circ - 16^\circ) \][/tex]
Since [tex]\(\cos x = \sin 16^\circ\)[/tex], by comparing both sides, we have:
[tex]\[ \cos x = \cos (90^\circ - 16^\circ) \][/tex]
Thus:
[tex]\[ x = 90^\circ - 16^\circ \][/tex]
Simplifying the expression:
[tex]\[ x = 74^\circ \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is [tex]\( \boxed{74^\circ} \)[/tex].
