Let cos α = sin β = 0.7046 and let 0° ≤ β ≤ 90°. If α =45.2°, what is the value in degrees of angle β?

Draw a right triangle in Q1.
Note that the sine of the base angle is the cosine of the vertex angle and vice versa. These two angles are complementary (add to 90°).

Thus sin(90-t) = cos(t),
sin(t) = cos(90-t).

This was well understood when trig functions were obtained from books of tables. These stopped at 45°. Sometimes there was an added column containing the complementary angle.

The sine of an angle is the cosine of its complement (when both are in the first quadrant).
.. β = 90° - 45.2° = 44.8°
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arcsin(0.7046) ≈ 44.8°