Calculus me solve this simple problem (I forgot how to): arcsin(4/5) = ?

[GreenPrint]

Homework Statement

how do I solve this

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?

Homework Equations

The Attempt at a Solution

 

[GreenPrint]

ok now this is an algebra 2 problem... I have goten far down to hear

e^(ix) = (4i +/- 3)/5

now how do I solve for x I feel really stupid now as this is algebra 2...

can't use natural log right or the common log as

ln( e^(ix) )
does not equal ix

so what do I do?

 

[GreenPrint]

Wait apparently I'm suppose to do something involving

log(z) = ln|z| + i arg(z) for complex numbers z

or something correct?

 

[hunt_mat]

Try it and see.