How do you find the exact value of #arcsin(1/3)#?
You get my answer, from my explanation.
In general, any value is transcendental. Yet, define units like
second, ounce, foot, dollar, ... and express values, rounded to
nearest unit .
In the values of arcsin that
say 0.1 rad = (0.1/pi ) 180^o = 5.729577951...^o is transcendental.
For that matter,
arcsin ( 1/3) = 19.47122063...^o = 0.339836836909... rad.
In my opinion, all irrational values are transcendental that defy
rational form ( integer )/( integer ).
In classification of real numbers, Foundation Mathematical
Philosophy is not firm.