We could use such LookUp tables since our input-values (the degrees) were equally distributed, so we could use them as the array-counter in the table.
In your case it would be more complicated.
If you use an equally distributed counter for the asin ( between -1 and 1 for example 400 values), your accuracy would not be the same for all output values.

I would use a lookup-table for sin and use it reverse, look thru all values in the table, the desired result is the indexof the closest value.
But I don't know if that would be faster than calculation!