I am attempting to learn inverse hyperbolic functions but I can't even follow the examples in the book. The example is $y= \sinh y = \frac{e^y - e^{-y}}2$ they they make it into $e^y -2x - e^{-y} = 0$ I don't really understand what is going on, are inverses equal to x? I just don't follow what he did there at all. There just isn't much explanation here, or at least enough for me to figure it out.
Inverse hyperbolic functions
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$\begingroup$
trigonometry
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2That should read $x = \mathrm{sinh} y$, so that $y=\mathrm{sinh}^{-1} x$ (the inverse hyperbolic sine function) is what you're solving for. And what they did is basically multiply both sides of the equation by $2$ and then move everything onto one side. – 2011-10-07
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0I stared at it for about 10 minutes and couldn't figure that out...either I am stupid or they should have just added that step. – 2011-10-07
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1Jordan, you shouldn't have to apologize or call yourself stupid. Maybe you are doomed to be forever bad at math, or maybe you have a lot more potential and just can't find the right rhythm - I don't have an answer to that. But it seriously pains me to see you beating yourself up all the time. – 2011-10-07
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1...and it's certainly unhealthy to be frequently, repeatedly calling yourself "stupid". Things like those, repeated enough, are self-fulfilling. You need to change that habit if you don't want to be forever stuck. – 2011-10-07