DLMF:4.21.E41 (Q1745)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:4.21.E41
No description defined

    Statements

    Defining formula
    | sin ⁡ z | = ( sin 2 ⁡ x + sinh 2 ⁡ y ) 1 / 2 = ( 1 2 ⁢ ( cosh ⁡ ( 2 ⁢ y ) - cos ⁡ ( 2 ⁢ x ) ) ) 1 / 2 , 𝑧 superscript 2 𝑥 2 𝑦 1 2 superscript 1 2 2 𝑦 2 𝑥 1 2 {\displaystyle{\displaystyle|\sin z|=({\sin^{2}}x+{\sinh^{2}}y)^{1/2}=\left(% \tfrac{1}{2}\left(\cosh\left(2y\right)-\cos\left(2x\right)\right)\right)^{1/2}% ,}}
    0 references
    DLMF id
    DLMF:4.21.E41
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aacdec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2addec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2addec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aabdec
    0 references
    Q11218
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C4.S1.XMD6.m1ddec
    0 references
    Q11222
    Defining formula
    y 𝑦 {\displaystyle{\displaystyle y}}
    xml-id
    C4.S1.XMD7.m1ddec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1wdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1745&oldid=27341"