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I've learned what $\sinh{x},\cosh{x}$ (the hyperbolic trig functions) are defined as formula, but how is it related to $\sin{x},\cos{x}?$
The only thing I've noticed is that $\cosh^2(x)-\sinh^2(x)=1.$

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marked as duplicate by user296602, Blue trigonometry Aug 31 '18 at 1:35

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They’re related by Euler’s formula. Since $e^{ix}=\cos x+i \sin x$ we have $e^{-ix}=\cos x-i \sin x$. This reveals,

$$\cosh (ix)=\cos x$$

$$\sinh (ix)=i \sin x$$

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