Elementary Functions - 4.14 Definitions and Periodicity
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| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 4.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit}}
\sin@@{z} = \frac{e^{\iunit z}-e^{-\iunit z}}{2\iunit} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sin(z) = (exp(I*z)- exp(- I*z))/(2*I)
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Sin[z] == Divide[Exp[I*z]- Exp[- I*z],2*I]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2}}
\cos@@{z} = \frac{e^{\iunit z}+e^{-\iunit z}}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(z) = (exp(I*z)+ exp(- I*z))/(2)
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Cos[z] == Divide[Exp[I*z]+ Exp[- I*z],2]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z}+ i\sin@@{z} = e^{+ iz}}
\cos@@{z}+ i\sin@@{z} = e^{+ iz} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(z)+ I*sin(z) = exp(+ I*z)
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Cos[z]+ I*Sin[z] == Exp[+ I*z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{z}- i\sin@@{z} = e^{- iz}}
\cos@@{z}- i\sin@@{z} = e^{- iz} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(z)- I*sin(z) = exp(- I*z)
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Cos[z]- I*Sin[z] == Exp[- I*z]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}}}
\tan@@{z} = \frac{\sin@@{z}}{\cos@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tan(z) = (sin(z))/(cos(z))
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Tan[z] == Divide[Sin[z],Cos[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@@{z} = \frac{1}{\sin@@{z}}}
\csc@@{z} = \frac{1}{\sin@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | csc(z) = (1)/(sin(z))
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Csc[z] == Divide[1,Sin[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@@{z} = \frac{1}{\cos@@{z}}}
\sec@@{z} = \frac{1}{\cos@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sec(z) = (1)/(cos(z))
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Sec[z] == Divide[1,Cos[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}}}
\cot@@{z} = \frac{\cos@@{z}}{\sin@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cot(z) = (cos(z))/(sin(z))
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Cot[z] == Divide[Cos[z],Sin[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}}}
\frac{\cos@@{z}}{\sin@@{z}} = \frac{1}{\tan@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (cos(z))/(sin(z)) = (1)/(tan(z))
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Divide[Cos[z],Sin[z]] == Divide[1,Tan[z]]
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Successful | Successful | - | Successful [Tested: 7] |
| 4.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{z+2k\pi} = \sin@@{z}}
\sin@{z+2k\pi} = \sin@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sin(z + 2*k*Pi) = sin(z)
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Sin[z + 2*k*Pi] == Sin[z]
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Successful | Failure | - | Successful [Tested: 21] |
| 4.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{z+2k\pi} = \cos@@{z}}
\cos@{z+2k\pi} = \cos@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(z + 2*k*Pi) = cos(z)
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Cos[z + 2*k*Pi] == Cos[z]
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Successful | Failure | - | Successful [Tested: 21] |
| 4.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{z+k\pi} = \tan@@{z}}
\tan@{z+k\pi} = \tan@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tan(z + k*Pi) = tan(z)
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Tan[z + k*Pi] == Tan[z]
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Successful | Failure | - | Successful [Tested: 21] |