numpy.sin

numpy.sin(x[, out]) = <ufunc 'sin'>

Trigonometric sine, element-wise.

Parameters :

x : array_like

Angle, in radians (

System Message: WARNING/2 (2 \pi)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

rad equals 360 degrees).

Returns :

y : array_like

The sine of each element of x.

See also

arcsin, sinh, cos

Notes

The sine is one of the fundamental functions of trigonometry (the mathematical study of triangles). Consider a circle of radius 1 centered on the origin. A ray comes in from the

System Message: WARNING/2 (+x)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

axis, makes an angle at the origin (measured counter-clockwise from that axis), and departs from the origin. The

System Message: WARNING/2 (y)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

coordinate of the outgoing ray’s intersection with the unit circle is the sine of that angle. It ranges from -1 for

System Message: WARNING/2 (x=3\pi / 2)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

to +1 for

System Message: WARNING/2 (\pi / 2.)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

The function has zeroes where the angle is a multiple of

System Message: WARNING/2 (\pi)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

. Sines of angles between

System Message: WARNING/2 (\pi)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

and

System Message: WARNING/2 (2\pi)

latex exited with error: [stderr] [stdout] This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012/TeX Live for SUSE Linux) restricted \write18 enabled. entering extended mode (./math.tex LaTeX2e <2011/06/27> Babel <v3.8m> and hyphenation patterns for english, dumylang, nohyphenation, ge rman-x-2011-07-01, ngerman-x-2011-07-01, afrikaans, ancientgreek, ibycus, arabi c, armenian, basque, bulgarian, catalan, pinyin, coptic, croatian, czech, danis h, dutch, ukenglish, usenglishmax, esperanto, estonian, ethiopic, farsi, finnis h, french, friulan, galician, german, ngerman, swissgerman, monogreek, greek, h ungarian, icelandic, assamese, bengali, gujarati, hindi, kannada, malayalam, ma rathi, oriya, panjabi, tamil, telugu, indonesian, interlingua, irish, italian, kurmanji, lao, latin, latvian, lithuanian, mongolian, mongolianlmc, bokmal, nyn orsk, polish, portuguese, romanian, romansh, russian, sanskrit, serbian, serbia nc, slovak, slovenian, spanish, swedish, turkish, turkmen, ukrainian, uppersorb ian, welsh, loaded. (/usr/share/texmf/tex/latex/base/article.cls Document Class: article 2007/10/19 v1.4h Standard LaTeX document class (/usr/share/texmf/tex/latex/base/size12.clo)) (/usr/share/texmf/tex/latex/base/inputenc.sty ! LaTeX Error: File `utf8x.def’ not found. Type X to quit or <RETURN> to proceed, or enter new name. (Default extension: def) Enter file name: ! Emergency stop. <read *> l.131 \endinput ^^M No pages of output. Transcript written on math.log.

are negative. The numerous properties of the sine and related functions are included in any standard trigonometry text.

Examples

Print sine of one angle:

>>> np.sin(np.pi/2.)
1.0

Print sines of an array of angles given in degrees:

>>> np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. )
array([ 0.        ,  0.5       ,  0.70710678,  0.8660254 ,  1.        ])

Plot the sine function:

>>> import matplotlib.pylab as plt
>>> x = np.linspace(-np.pi, np.pi, 201)
>>> plt.plot(x, np.sin(x))
>>> plt.xlabel('Angle [rad]')
>>> plt.ylabel('sin(x)')
>>> plt.axis('tight')
>>> plt.show()

(Source code, png, pdf)