# Show that arcsin(2) is

1. May 16, 2013

### Craptola

Got a maths exam tomorrow been looking through some past papers. Have hit a stumbling block with regard to complex numbers, the problem lies with my algebra.

1. The problem statement, all variables and given/known data
Show that $\arcsin(2) = \frac{\pi}{2}-i\ln (2\pm \sqrt3)$

2. Relevant equations
I'm fairly certain the way to solve this is to use
$$\sin(z)=\frac{1}{2i}(e^{iz}- e^{-iz})$$

3. The attempt at a solution
Equating sin(z) to 2 I could only rearrange it to

$$4i=e^{iz}-e^{-iz}$$
I was always pretty awful at algebra and can't see a way to rearrange for z. If anyone could nudge me in the right direction it would be greatly appreciated.

2. May 16, 2013

### Hypersphere

The problem becomes simpler if you make the substitution $v=e^{iz}$.

3. May 16, 2013

### haruspex

When the question says "show that a=b", it gives you the option of working from the other end.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted