Why sinh, cosh, and tanh relate to hyperbolas

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lch7
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Will someone help me to understand sinh, cosh, and tanh. I know they have some relevance to hyperbolas and trigonometric identities. Thank you.
 
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The main reason to use these is to give a shortcut for derivatives of variations of e functions. There is no need to learn these until calc and not. even necessaru for calc since you can always do it out instead of wrote memorization.