To solve for [tex]\( f \)[/tex] in the equation [tex]\( \cos(22f - 1) = \sin(7f + 4) \)[/tex], we can utilize the trigonometric identity which states that [tex]\(\cos(\theta) = \sin(90^\circ - \theta)\)[/tex].
Using this identity, we can rewrite the equation as:
[tex]\[ \cos(22f - 1) = \sin(7f + 4) \][/tex]
This implies that:
[tex]\[ 22f - 1 = 90^\circ - (7f + 4) \][/tex]
Now, let's solve for [tex]\( f \)[/tex]:
\begin{align}
22f - 1 &= 90^\circ - 7f - 4 \\
22f - 1 &= 86^\circ - 7f \\
22f + 7f &= 86^\circ + 1 \\
29f &= 87^\circ \\
f &= \frac{87^\circ}{29} \\
f &= 3
\end{align}
Thus, checking the possible values given in the original problem, we see that the only value that satisfies the condition [tex]\( 0 < f \leq 90 \)[/tex] and correctly fits our equation is:
[tex]\[ \boxed{3} \][/tex]
