What is the difference between arcsin and sin^-1 ?

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Both refer to the inverse sine function.

The inverse sine (or arcsine) of x:



where x is a real number in the domain of the function:



and the arcsine function returns an angle in the interval 



So if you see anywhere one of these expressions below



then you should look for an angle that satisfies the following conditions:



This angle is called the inverse sine of the real number x.

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Pay attention and do not mistake the arcsine function for the reciprocal of sine (which is cosecant); especially if you prefer or see that notation with an superscript -1. This one can be easily mistaken for an exponent:



but the reciprocal is something like



and this last one has a total different meaning.

I hope this helps. =)

The answers are 20,30,80,180,960,890,1230,4560. on the first row