Difference between revisions of "Relationship between arcsin and arccsc"
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| − | + | ==Theorem== | |
| − | + | The following formula holds: | |
$$\mathrm{arcsin}(z) = \mathrm{arccsc}\left( \dfrac{1}{z} \right),$$ | $$\mathrm{arcsin}(z) = \mathrm{arccsc}\left( \dfrac{1}{z} \right),$$ | ||
where $\mathrm{arcsin}$ denotes the [[arcsin|inverse sine]] function and $\mathrm{arccsc}$ denotes the [[arccsc|inverse cosecant]] function. | where $\mathrm{arcsin}$ denotes the [[arcsin|inverse sine]] function and $\mathrm{arccsc}$ denotes the [[arccsc|inverse cosecant]] function. | ||
| − | + | ||
| − | + | ==Proof== | |
| − | + | ||
| − | + | ==References== | |
| + | |||
| + | [[Category:Theorem]] | ||
| + | [[Category:Unproven]] | ||
Latest revision as of 07:28, 8 June 2016
Theorem
The following formula holds: $$\mathrm{arcsin}(z) = \mathrm{arccsc}\left( \dfrac{1}{z} \right),$$ where $\mathrm{arcsin}$ denotes the inverse sine function and $\mathrm{arccsc}$ denotes the inverse cosecant function.
