DLMF:4.24.E16 (Q1810): Difference between revisions

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Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: general arccosine function / rank
 
Normal rank
Property / Symbols used: general arccosine function / qualifier
 
Defining formula:

Arccos z multivalued-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccos}\NVar{z}}}

\Acos@@{\NVar{z}}
Property / Symbols used: general arccosine function / qualifier
 
xml-id: C4.S23.E2.m2aadec

Revision as of 18:39, 1 January 2020

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DLMF:4.24.E16
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    Arcsin u ± Arccos v = Arcsin ( u v ± ( ( 1 - u 2 ) ( 1 - v 2 ) ) 1 / 2 ) = Arccos ( v ( 1 - u 2 ) 1 / 2 u ( 1 - v 2 ) 1 / 2 ) , plus-or-minus multivalued-inverse-sine 𝑢 multivalued-inverse-cosine 𝑣 multivalued-inverse-sine plus-or-minus 𝑢 𝑣 superscript 1 superscript 𝑢 2 1 superscript 𝑣 2 1 2 multivalued-inverse-cosine minus-or-plus 𝑣 superscript 1 superscript 𝑢 2 1 2 𝑢 superscript 1 superscript 𝑣 2 1 2 {\displaystyle{\displaystyle\operatorname{Arcsin}u\pm\operatorname{Arccos}v=% \operatorname{Arcsin}\left(uv\pm((1-u^{2})(1-v^{2}))^{1/2}\right)=% \operatorname{Arccos}\left(v(1-u^{2})^{1/2}\mp u(1-v^{2})^{1/2}\right),}}
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    DLMF:4.24.E16
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    Arccos z multivalued-inverse-cosine 𝑧 {\displaystyle{\displaystyle\operatorname{Arccos}\NVar{z}}}
    C4.S23.E2.m2aadec
    0 references