Let's solve each part of the question step-by-step:
### 1. [tex]\(\sin(28^\circ)\)[/tex]
We are asked to find a relation involving [tex]\(\sin(28^\circ)\)[/tex]. Recall that:
[tex]\[
\sin(x) = \cos(90^\circ - x)
\][/tex]
Thus:
[tex]\[
\sin(28^\circ) = \cos(62^\circ)
\][/tex]
The numerical value is:
[tex]\[
\sin(28^\circ) \approx 0.46947156278589086
\][/tex]
### 2. [tex]\(\cos(33^\circ)\)[/tex]
Similarly, for this part, we need to recall that:
[tex]\[
\cos(x) = \sin(90^\circ - x)
\][/tex]
Therefore:
[tex]\[
\cos(33^\circ) = \sin(57^\circ)
\][/tex]
The numerical value is:
[tex]\[
\cos(33^\circ) \approx 0.838670567945424
\][/tex]
### 3. [tex]\(\cos(31^\circ)\)[/tex]
Using the same identity:
[tex]\[
\cos(31^\circ) = \sin(59^\circ)
\][/tex]
The numerical value is:
[tex]\[
\cos(31^\circ) \approx 0.8571673007021123
\][/tex]
### 4. [tex]\(\cos(90^\circ - \theta)\)[/tex]
For the final part, we apply the identity directly concerning [tex]\(\theta\)[/tex]:
[tex]\[
\cos(90^\circ - \theta) = \sin(\theta)
\][/tex]
By rewriting each part, our final results are:
[tex]\[
\begin{array}{l}
\sin (28^\circ)=\cos (62^\circ) \approx 0.46947156278589086, \\
\cos (33^\circ)=\sin (57^\circ) \approx 0.838670567945424, \\
\cos (31^\circ)=\sin (59^\circ) \approx 0.8571673007021123, \\
\cos (90^\circ-\theta)=\sin (\theta)
\end{array}
\][/tex]
This completes our solution for each requested trigonometric relation.
