I need help in understanding how Jacobian Elliptic Functions are interpreted as inverses of Elliptic Functions.(adsbygoogle = window.adsbygoogle || []).push({});

Please reference the wiki page on Jacobian Elliptic functions:

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

For example, if $$u=u(φ,m)$$ is defined as $$u(φ,m) = \int_0^φ \frac{1}{ \sqrt{1-m sin^2(θ)}} \, dθ$$

where ##φ## is the amplitude $$φ=am(u)$$

Then $$y'=sin(φ)$$ is defined to be the Jacobian function $$sn(u,m)$$ or $$sin(φ)=sn(u,m)$$

I understand that the Jacobian functions are defined as inverses to the elliptic integrals. Bug where does the ##sin(φ)## come from? I think I am getting getting lost with all of the different variables. Can someone explain in as clearly as possible? Any insight would be appreciated. Thanks!

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# A Jacobian Elliptic Functions as Inverse Elliptic Functions

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