Revision as of 22:24, 8 June 2025 edit Rgdboer (talk \| contribs) Autopatrolled, Extended confirmed users, Pending changes reviewers 18,111 edits →Definitions: image for sinh and cosh ← Previous edit		Revision as of 13:28, 9 June 2025 edit undo Opkulk (talk \| contribs) 2 edits →Inverse functions as logarithms: Added content. Tags: Reverted Mobile edit Mobile web edit Next edit →
Line 224: \operatorname {arcoth} (x) &= \frac{1}{2}\ln \left( \frac{x + 1}{x - 1} \right) && \|x\| > 1 \\ \operatorname {arsech} (x) &= \ln \left( \frac{1}{x} + \sqrt{\frac{1}{x^2} - 1}\right) = \ln \left( \frac{1+ \sqrt{1 - x^2}}{x} \right) && 0 < x \leq 1 \\ \operatorname {arcsch} (x) &= \ln \left( \frac{1}{x} + \sqrt{\frac{1}{x^2} +1}\right) &&= \ln\left( \frac{1 + \sqrt{1 + x^2}}{\|x\|} \neright) 0\cdot \operatorname{sgn}(x) && x \ne 0 \end{align}</math>

Hyperbolic functions: Difference between revisions