sin x = 2

http://www.wolframalpha.com/input/?i=arcsin+2
Apparently sin(pi/2 +- i*ln(2+sqrt3)) = 2.

Where the heck did you get that from? o.O

This is the form I'm most familiar with... I'll see what I can dig up on it.


First, we start with what the derivative of arcsin of x is.

Code:

y = arcsin(x)
sin(y) = x
y'cos(y) = 1 <---derivation step
y' = 1/cos(y)
y' = 1/cos(arcsin(x))
y' = 1/sqrt(1-x^2)

General integration formula:
arcsin(a*x) = ʃ(1/sqrt(1-a^2*x^2) * dx)

I'm pretty sure I lost most of you already o.o But we have a workable formula that doesn't involve weird mystery symbols such as sin or ln. To me, this makes the problem of perspective much easier to handle. But if we took it just the way it is, we'll just get arcsin again. So let's do a trick or two...

Code:

ʃ(1/sqrt(1-a^2*x^2) * dx) = ʃ(1/(sqrt(1-a*x)*sqrt(1+a*x)))
Integration by parts

Okay, now I'm not motivated anymore >_>