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[tex]\displaystyle \\ \arcsin(0.58) \approx \arcsin(0.5) = \arcsin \Big( \frac{1}{2} \Big)= 30^o \\ \\ \Longrightarrow ~~\arcsin(0.58) \approx \boxed{30^o} \\ \\ \texttt{Verification:} \\ \\ \sin(30^o)= \frac{1}{2} = 0.5 \approx 0.58[/tex]