My question as follows derives from:

sin(x)=a/c;

given values a=3 and c=5 just for examples sake:

sin(x)=3/5=0.6.

ok, so my question is, knowing the sine of the angle i would like to calculate the angle in degrees and in radians.

The trick is I don't want to use a calculator.

I'm guessing there is an algorithm to calculate the angle. What is it and how would it be applied to my example?