List questions from hyperbolic-functions

Published on 14 Apr 2026 - 7:27

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Proving that a function is invertible

Published on 13 Apr 2026 - 10:41

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Prove that $\sin(z) =\frac{e^{iz}-e^{-iz}}{2i} =\sin(x)\cosh(y) +i\cos(x)\sinh(y)$

Published on 13 Apr 2026 - 17:24

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sech(x) inverse for x< 0

Published on 10 May 2026 - 13:24

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Hyperbolic substitution in $\int\frac{dx}{\sqrt{x^2-a^2}}$ for $x\le -a$

Published on 14 Apr 2026 - 10:36

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Geometric intuition of composition of hyperbolic and inverse hyperbolic trig functions

Published on 13 Apr 2026 - 22:37

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How to find $\lim_{n\rightarrow \infty}\frac{1}{n}\prod^{n-1}_{k=1} \left( \frac{x^2}{n^2}-2(\cos\left(\frac{k \pi}{n}\right)-1)\right)$

Published on 17 Apr 2026 - 15:32

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An integral involving a hyperbolic secant function and a Gaussian

Published on 10 May 2026 - 14:52

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Covering a Hyperbolic Right-Angled Hexagon

Published on 17 Apr 2026 - 14:30

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Eliminate $z$ from these two hyperbolic functions.

Published on 08 Apr 2026 - 19:28

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Asymptote for $y=±\sqrt{x^2-1}$

Published on 15 Apr 2026 - 6:04

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Can the hyperbolic cotangent be defined in terms of the projection of an intersection?

Published on 11 Apr 2026 - 4:41

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How to solve $0 = \cos x − \cosh x + 1$?

Published on 14 Apr 2026 - 15:05

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Simplifying $\operatorname{tanh}(\operatorname{arsinh}(x))$

Published on 14 Apr 2026 - 18:54

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First step for $\int\frac{\operatorname{gd}\left(\log x\right)}{\sqrt{1-x^2}}dx$, where $\operatorname{gd}(x)$ denotes the Gudermannian function

Published on 15 Apr 2026 - 20:29

List Question

Differentiate $\cosh^2(2x)$

Proving that a function is invertible

Prove that $\sin(z) =\frac{e^{iz}-e^{-iz}}{2i} =\sin(x)\cosh(y) +i\cos(x)\sinh(y)$

sech(x) inverse for x< 0

Hyperbolic substitution in $\int\frac{dx}{\sqrt{x^2-a^2}}$ for $x\le -a$

Geometric intuition of composition of hyperbolic and inverse hyperbolic trig functions

How to find $\lim_{n\rightarrow \infty}\frac{1}{n}\prod^{n-1}_{k=1} \left( \frac{x^2}{n^2}-2(\cos\left(\frac{k \pi}{n}\right)-1)\right)$

An integral involving a hyperbolic secant function and a Gaussian

Covering a Hyperbolic Right-Angled Hexagon

Eliminate $z$ from these two hyperbolic functions.

Asymptote for $y=±\sqrt{x^2-1}$

Can the hyperbolic cotangent be defined in terms of the projection of an intersection?

How to solve $0 = \cos x − \cosh x + 1$?

Simplifying $\operatorname{tanh}(\operatorname{arsinh}(x))$

First step for $\int\frac{\operatorname{gd}\left(\log x\right)}{\sqrt{1-x^2}}dx$, where $\operatorname{gd}(x)$ denotes the Gudermannian function

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