How is arctan(sinh(x∗pi)) the inverse of log(tan(x))/pi How is arctan(sinh(x∗pi)) the inverse of log(tan(x))/pi What is the relationship between log(x) and sinh(x). I guess is what my real question is.

Kubaczynjo

Kubaczynjo

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2022-08-31

How is arctan ( sinh ( x π ) ) the inverse of log ( tan ( x ) ) / π
How is
arctan ( sinh ( x π ) )
the inverse of
log ( tan ( x ) ) π
What is the relationship between log ( x ) and sinh ( x ). I guess is what my real question is.

Answer & Explanation

blerbintiy0

blerbintiy0

Beginner2022-09-01Added 8 answers

It's not. The inverse of your function y ( x ) = arctan ( sinh ( π x ) ) is y 1 ( x ) = sinh 1 ( tan y ) π , where sinh 1 ( t ) = ln ( t + t 2 + 1 )

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