Find Real Value of sin(i) Without i

[TheCanadian]

I am calculating a value and want to find the real value of sin(i). I can use series expansion and only take the terms without i (correct?) but is there any nicer way to express the result of taking the real value of sin(i)?

 

[micromass]

https://en.wikipedia.org/wiki/Hyperbolic_function

 

[TheCanadian]

https://en.wikipedia.org/wiki/Hyperbolic_function

I used the imaginary exponentials and found $\sin(i) = \frac{e^{-1} - e}{2i}$ but this seems purely imaginary...from the sum expansion of sin, it appeared that there were real values for the even power terms. Any advice you have for addressing what I am missing here since I'm looking for the real value would be great!

 

[micromass]

Indeed, $\sin(i)$ is purely imaginary. If you look at the series expansion of $\sin(i)$, you'll see that only $i^{\text{odd power}}$ appear in this expansion. And as you know, $i^{\text{odd power}} = \pm i$.