how do I solve this

Question

arcsin(4/5)

note that I am not looking for about 53 degrees

I believe I'm suppose to solve euler's formula for x

i.e.
sin (x) = (e^(ix) - e^(-ix))/(2i)
where x is in radians
hence I would do something like this

sin (x) = (e^(ix) - e^(-ix))/(2i) = 4/5

(e^(ix) - e^(-ix))/(2i) = 4/5
solve the equation above for x

this is were I need help if somebody could just show me quickly how to do this that would be great!!!

If I remeber correctly I need to use cis(x) or something right?

Answer 1

ok this is now an algebra question...

Answer 2

x = 0.92730.. radians

I don't see any way to do this algebraically.