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can anyone simplify, $\sin^{-1}\tanh\theta=?$ in a better equation?

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i see no equation –  Dominic Michaelis Mar 6 '13 at 9:30
    
I think, you missed an $=$-sign and something on the right hand side of the equation. –  born Mar 6 '13 at 9:32
    
and i see an expression –  Aang Mar 6 '13 at 9:32
    
@Dominic Michaelis can solve it $\sin^{-1}\tanh\theta=?$ –  Neo Mar 6 '13 at 9:32
    
nope ? is not in the image of $\sin^{-1}$ i am afraid –  Dominic Michaelis Mar 6 '13 at 9:33
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2 Answers

up vote 3 down vote accepted

You are looking for the Gudermannian function. See Wikipedia or Mathworld.

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ok thank you. so $\sinh^{-1}\tan x$ is The inverse Gudermannian function, –  Neo Mar 6 '13 at 13:07
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$\sin^{-1}\tanh x=2{\tan^{-1} \tanh x} \cosh x \sqrt {\operatorname{sech}^2 x}$

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