{
  "__type": "IngestedDoc",
  "__tag": 4010,
  "_content": {
    "Notes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "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 "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "+x"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " axis, makes an angle at the origin (measured counter-clockwise from that axis), and departs from the origin.  The "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "y"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " coordinate of the outgoing ray's intersection with the unit circle is the sine of that angle.  It ranges from -1 for "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "x=3\\pi / 2"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " to +1 for "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\pi / 2."
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "  The function has zeroes where the angle is a multiple of "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\pi"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": ". Sines of angles between "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "\\pi"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " and "
            },
            {
              "__type": "InlineMath",
              "__tag": 4057,
              "value": "2\\pi"
            },
            {
              "__type": "Text",
              "__tag": 4046,
              "value": " are negative. The numerous properties of the sine and related functions are included in any standard trigonometry text."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Raises": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Yields": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Methods": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Returns": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "y",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "The sine of each element of x. This is a scalar if "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "x",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": null,
                        "version": null,
                        "kind": "local",
                        "path": "x"
                      },
                      "kind": "local"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " is a scalar."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Paragraph",
          "__tag": 4045,
          "children": [
            {
              "__type": "Text",
              "__tag": 4046,
              "value": "Trigonometric sine, element-wise."
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Receives": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Warnings": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Attributes": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [
        {
          "__type": "Parameters",
          "__tag": 4026,
          "children": [
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "x",
              "annotation": "array_like",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "Angle, in radians ("
                    },
                    {
                      "__type": "InlineMath",
                      "__tag": 4057,
                      "value": "2 \\pi"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " rad equals 360 degrees)."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "out",
              "annotation": "ndarray, None, or tuple of ndarray and None, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "A location into which the result is stored. If provided, it must have a shape that the inputs broadcast to. If not provided or None, a freshly-allocated array is returned. A tuple (possible only as a keyword argument) must have length equal to the number of outputs."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "where",
              "annotation": "array_like, optional",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "This condition is broadcast over the input. At locations where the condition is True, the "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "out",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": null,
                        "version": null,
                        "kind": "local",
                        "path": "out"
                      },
                      "kind": "local"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " array will be set to the ufunc result. Elsewhere, the "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "out",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": null,
                        "version": null,
                        "kind": "local",
                        "path": "out"
                      },
                      "kind": "local"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " array will retain its original value. Note that if an uninitialized "
                    },
                    {
                      "__type": "CrossRef",
                      "__tag": 4002,
                      "value": "out",
                      "reference": {
                        "__type": "RefInfo",
                        "__tag": 4000,
                        "module": null,
                        "version": null,
                        "kind": "local",
                        "path": "out"
                      },
                      "kind": "local"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": " array is created via the default "
                    },
                    {
                      "__type": "InlineCode",
                      "__tag": 4051,
                      "value": "out=None"
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": ", locations within it where the condition is False will remain uninitialized."
                    }
                  ]
                }
              ]
            },
            {
              "__type": "DocParam",
              "__tag": 4016,
              "name": "**kwargs",
              "annotation": "",
              "desc": [
                {
                  "__type": "Paragraph",
                  "__tag": 4045,
                  "children": [
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "For other keyword-only arguments, see the "
                    },
                    {
                      "__type": "InlineRole",
                      "__tag": 4003,
                      "value": "ufunc docs <ufuncs.kwargs>",
                      "domain": null,
                      "role": "ref",
                      "inventory": null
                    },
                    {
                      "__type": "Text",
                      "__tag": 4046,
                      "value": "."
                    }
                  ]
                }
              ]
            }
          ]
        }
      ],
      "title": [],
      "level": 0,
      "target": null
    },
    "Extended Summary": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    },
    "Other Parameters": {
      "__type": "Section",
      "__tag": 4015,
      "children": [],
      "title": [],
      "level": 0,
      "target": null
    }
  },
  "_ordered_sections": [
    "Summary",
    "Extended Summary",
    "Parameters",
    "Attributes",
    "Methods",
    "Returns",
    "Yields",
    "Receives",
    "Other Parameters",
    "Raises",
    "Warns",
    "Warnings",
    "Notes"
  ],
  "item_file": "/numpy/__init__.py",
  "item_line": null,
  "item_type": "ufunc",
  "aliases": [
    "numpy.sin"
  ],
  "example_section_data": {
    "__type": "Section",
    "__tag": 4015,
    "children": [
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import numpy as np\n",
        "execution_status": "success"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nPrint sine of one angle:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.sin(np.pi/2.)\n",
        "execution_status": "failure"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nPrint sines of an array of angles given in degrees:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "np.sin(np.array((0., 30., 45., 60., 90.)) * np.pi / 180. )\n",
        "execution_status": "failure"
      },
      {
        "__type": "Text",
        "__tag": 4046,
        "value": "\nPlot the sine function:\n\n"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "import matplotlib.pylab as plt\nx = np.linspace(-np.pi, np.pi, 201)\n",
        "execution_status": "success"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.plot(x, np.sin(x))\nplt.xlabel('Angle [rad]')\nplt.ylabel('sin(x)')\nplt.axis('tight')\n",
        "execution_status": "failure"
      },
      {
        "__type": "Code",
        "__tag": 4050,
        "value": "plt.show()\n",
        "execution_status": "success"
      },
      {
        "__type": "Figure",
        "__tag": 4024,
        "value": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "numpy",
          "version": "2.4.4",
          "kind": "assets",
          "path": "fig-b26d3eed5b81223d.png"
        }
      }
    ],
    "title": [],
    "level": 0,
    "target": null
  },
  "see_also": [
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "arcsin",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "arcsin"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "cos",
        "reference": {
          "__type": "RefInfo",
          "__tag": 4000,
          "module": "current-module",
          "version": "current-version",
          "kind": "to-resolve",
          "path": "cos"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    },
    {
      "__type": "SeeAlsoItem",
      "__tag": 4028,
      "name": {
        "__type": "CrossRef",
        "__tag": 4002,
        "value": "sinh",
        "reference": {
          "__type": "LocalRef",
          "__tag": 4022,
          "kind": "module",
          "path": "numpy:sinh"
        },
        "kind": "module"
      },
      "descriptions": [],
      "type": null
    }
  ],
  "signature": null,
  "references": null,
  "qa": "numpy:sin",
  "arbitrary": [],
  "local_refs": [
    "**kwargs",
    "out",
    "where",
    "x",
    "y"
  ]
}