Difference between revisions of "Relationship between sine, Gudermannian, and tanh"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\sin(\mathrm{gd}(x))=\tanh(x),$$ | $$\sin(\mathrm{gd}(x))=\tanh(x),$$ | ||
where $\sin$ denotes the [[sine]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\tanh$ denotes the [[tanh|hyperbolic tangent]]. | where $\sin$ denotes the [[sine]], $\mathrm{gd}$ denotes the [[Gudermannian]], and $\tanh$ denotes the [[tanh|hyperbolic tangent]]. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
Revision as of 00:41, 4 June 2016
Theorem
The following formula holds: $$\sin(\mathrm{gd}(x))=\tanh(x),$$ where $\sin$ denotes the sine, $\mathrm{gd}$ denotes the Gudermannian, and $\tanh$ denotes the hyperbolic tangent.
