The Gudermannian functionality provides a immediate relationship in between the round functions along with the hyperbolic kinds that does not contain complicated numbers.
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e i x = cos x + i sin x e − i x = cos x − i sin x displaystyle commence aligned e^ ix &=cos x+i;sin xe^ -ix &=cos x-i;sin xconclude aligned
The hyperbolic capabilities could be defined as answers of differential equations: The hyperbolic get redirected here sine and cosine are definitely the special Option (s, c) on the system
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