1

Is there a form of $e^{\sin(x)}$ that does not have trig functions in the exponent? I've seen the "Euler Identity" form and looked into series expansions. (thanks for the answers -- sorry I didn't give background earlier.) I'm curious if there was something computationally faster than sin() then exp().

Paul
  • 111
  • It is possible to rewrite it without using the symbol $\sin$ (see this), but by its very nature $\sin$ will always be there, whether you see it or not. – Git Gud Mar 10 '14 at 14:34

1 Answers1

2

You could use this $$ e^{\sin(x)} = e^{\frac{1}{2i}(e^{ix} - e^{-ix})} $$ But I doubt that's what you're looking for. A common trick in situations like this is to use the taylor series. So you could try $$ e^{\sin(x)} = e^{x-x^3/6 + x^5/120 - \cdots} $$ or $$ e^{\sin(x)} = 1 + \sin(x) + \sin^2(x)/2 + \sin^{3}(x)/6 + \cdots $$

Ben Grossmann
  • 225,327