Difference between revisions of "Relationship between tangent, Gudermannian, and sinh"
From specialfunctionswiki
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The following formula holds: | The following formula holds: | ||
$$\tan(\mathrm{gd}(x))=\sinh(x),$$ | $$\tan(\mathrm{gd}(x))=\sinh(x),$$ | ||
| − | where $\tan$ denotes | + | where $\tan$ denotes [[tangent]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\sinh$ denotes the [[sinh|hyperbolic sine]]. |
==Proof== | ==Proof== | ||
Latest revision as of 02:42, 21 December 2016
Theorem
The following formula holds: $$\tan(\mathrm{gd}(x))=\sinh(x),$$ where $\tan$ denotes tangent, $\mathrm{gd}$ denotes the Gudermannian, and $\sinh$ denotes the hyperbolic sine.
