Arcsin equation - getting results?

[Sparky_]

Regarding the arcsine function and the complex variables approach:

z = sin(w)

w = -i*ln(iz +/- SQRT(1-z^2))

I'm trying to plug in numbers for z and "turn the crank" and get back the angle.

Meaning, if z = 0.5, the equation should yield 0.5236 (30 degrees) and if z = 0.707, I should get 0.7854 (45 degrees).

I've tried to do this in Excel. - no luck

I was assuming the "i" terms shifted things ?perhaps by PI/2? - no combination has worked.

How does this equation yield arcsine values? How do I turn the crank and handle the "i" terms.

Thanks
Sparky_

 

[HallsofIvy]

Regarding the arcsine function and the complex variables approach:

z = sin(w)

w = -i*ln(iz +/- SQRT(1-z^2))

I'm trying to plug in numbers for z and "turn the crank" and get back the angle.

Meaning, if z = 0.5, the equation should yield 0.5236 (30 degrees) and if z = 0.707, I should get 0.7854 (45 degrees).

? My TI-83 gives 0.523598... for z= 0.5 and 0.785398... for z= sqrt(2)/2 using your formula.

I've tried to do this in Excel. - no luck

I was assuming the "i" terms shifted things ?perhaps by PI/2? - no combination has worked.

How does this equation yield arcsine values? How do I turn the crank and handle the "i" terms.

Thanks
Sparky_

 

[Sparky_]

I'm curious how I can implement this equation manually. (pencil and paper of sorts)

I set this up in Excel (I know this is not pencil and paper)

I have a column for radians, I have a column that takes the sin() of that coumn, than I use Excel's Arcsin() function and take the arcsin of the sin() and then I have a column using the complex variables formula w = -i*ln(iz +/- SQRT(1-z^2)).

My hope is to have the 2 columns match - the column using the actual arcsin() function and the complex var. equation.

The complex variables formula uses simple operations that could be performed manually. I'm trying to understand how to do it manually and how to deal with the "i" terms since my attempts have failed. I thought the "i" terms would simply shift things by pi/2 or something like that.


Thanks
Sparky_