Path: blob/main/py-polars/docs/source/reference/sql/functions/trigonometry.rst
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Trigonometry
============
.. list-table::
:header-rows: 1
:widths: 20 60
* - :ref:`ACOS <acos>`
- Compute inverse cosine of the input column (in radians).
* - :ref:`ACOSD <acosd>`
- Compute inverse cosine of the input column (in degrees).
* - :ref:`ASIN <asin>`
- Compute inverse sine of the input column (in radians).
* - :ref:`ASIND <asind>`
- Compute inverse sine of the input column (in degrees).
* - :ref:`ATAN <atan>`
- Compute inverse tangent of the input column (in radians).
* - :ref:`ATAND <atand>`
- Compute inverse tangent of the input column (in degrees).
* - :ref:`ATAN2 <atan2>`
- Compute the inverse tangent of column_1/column_2 (in radians).
* - :ref:`ATAN2D <atan2d>`
- Compute the inverse tangent of column_1/column_2 (in degrees).
* - :ref:`COT <cot>`
- Compute the cotangent of the input column (in radians).
* - :ref:`COTD <cotd>`
- Compute cotangent of the input column (in degrees).
* - :ref:`COS <cos>`
- Compute the cosine of the input column (in radians).
* - :ref:`COSD <cosd>`
- Compute the cosine of the input column (in degrees).
* - :ref:`DEGREES <degrees>`
- Convert between radians and degrees.
* - :ref:`RADIANS <radians>`
- Convert between degrees and radians.
* - :ref:`SIN <sin>`
- Compute the sine of the input column (in radians).
* - :ref:`SIND <sind>`
- Compute the sine of the input column (in degrees).
* - :ref:`TAN <tan>`
- Compute the tangent of the input column (in radians).
* - :ref:`TAND <tand>`
- Compute the tangent of the input column (in degrees).
.. _acos:
ACOS
----
Compute inverse cosine of the input column (in radians).
**Example:**
.. code-block:: python
df = pl.DataFrame({"rads": [-1.0, -0.5, 0.5, 1.0]})
df.sql("SELECT rads, ACOS(rads) AS acos FROM self")
# shape: (4, 2)
# ┌──────┬──────────┐
# │ rads ┆ acos │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪══════════╡
# │ -1.0 ┆ 3.141593 │
# │ -0.5 ┆ 2.094395 │
# │ 0.5 ┆ 1.047198 │
# │ 1.0 ┆ 0.0 │
# └──────┴──────────┘
.. _acosd:
ACOSD
-----
Compute inverse cosine of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [-0.5, 0.0, 0.5]})
df.sql("SELECT degs, ACOSD(degs) AS acosd FROM self")
# shape: (3, 2)
# ┌──────┬───────┐
# │ degs ┆ acosd │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪═══════╡
# │ -0.5 ┆ 120.0 │
# │ 0.0 ┆ 90.0 │
# │ 0.5 ┆ 60.0 │
# └──────┴───────┘
.. _asin:
ASIN
----
Compute inverse sine of the input column (in radians).
**Example:**
.. code-block:: python
df = pl.DataFrame({"rads": [-1.0, -0.75, -0.0, 0.5]})
df.sql("SELECT rads, ASIN(rads) AS asin FROM self")
# shape: (4, 2)
# ┌───────┬───────────┐
# │ rads ┆ asin │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞═══════╪═══════════╡
# │ -1.0 ┆ -1.570796 │
# │ -0.75 ┆ -0.848062 │
# │ -0.0 ┆ -0.0 │
# │ 0.5 ┆ 0.523599 │
# └───────┴───────────┘
.. _asind:
ASIND
-----
Compute inverse sine of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [-0.5, 0.0, 0.5]})
df.sql("SELECT degs, ASIND(degs) AS asind FROM self")
# shape: (3, 2)
# ┌──────┬───────┐
# │ degs ┆ asind │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪═══════╡
# │ -0.5 ┆ -30.0 │
# │ 0.0 ┆ 0.0 │
# │ 0.5 ┆ 30.0 │
# └──────┴───────┘
.. _atan:
ATAN
----
Compute inverse tangent of the input column (in radians).
**Example:**
.. code-block:: python
df = pl.DataFrame({"rads": [-1.0, 0.0, 1.0, 2.0]})
df.sql("SELECT rads, ATAN(rads) AS atan FROM self")
# shape: (4, 2)
# ┌──────┬───────────┐
# │ rads ┆ atan │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪═══════════╡
# │ -1.0 ┆ -0.785398 │
# │ 0.0 ┆ 0.0 │
# │ 1.0 ┆ 0.785398 │
# │ 2.0 ┆ 1.107149 │
# └──────┴───────────┘
.. _atand:
ATAND
-----
Compute inverse tangent of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [-1.0, 0.0, 1.0]})
df.sql("SELECT degs, ATAND(degs) AS atand FROM self")
# shape: (3, 2)
# ┌──────┬───────┐
# │ degs ┆ atand │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪═══════╡
# │ -1.0 ┆ -45.0 │
# │ 0.0 ┆ 0.0 │
# │ 1.0 ┆ 45.0 │
# └──────┴───────┘
.. _atan2:
ATAN2
-----
Compute the inverse tangent of column_1/column_2 (in radians).
**Example:**
.. code-block:: python
df = pl.DataFrame(
{
"a": [-2.0, -1.0, 1.0, 2.0],
"b": [1.5, 1.0, 0.5, 0.0],
}
)
df.sql("SELECT a, b, ATAN2(a, b) AS atan2_ab FROM self")
# shape: (4, 3)
# ┌──────┬─────┬───────────┐
# │ a ┆ b ┆ atan2_ab │
# │ --- ┆ --- ┆ --- │
# │ f64 ┆ f64 ┆ f64 │
# ╞══════╪═════╪═══════════╡
# │ -2.0 ┆ 1.5 ┆ -0.927295 │
# │ -1.0 ┆ 1.0 ┆ -0.785398 │
# │ 1.0 ┆ 0.5 ┆ 1.107149 │
# │ 2.0 ┆ 0.0 ┆ 1.570796 │
# └──────┴─────┴───────────┘
.. _atan2d:
ATAN2D
------
Compute the inverse tangent of column_1/column_2 (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame(
{
"a": [-1.0, 0.0, 1.0, 1.0],
"b": [1.0, 1.0, 0.0, -1.0],
}
)
df.sql("SELECT a, b, ATAN2D(a, b) AS atan2d_ab FROM self")
# shape: (4, 3)
# ┌──────┬──────┬───────────┐
# │ a ┆ b ┆ atan2d_ab │
# │ --- ┆ --- ┆ --- │
# │ f64 ┆ f64 ┆ f64 │
# ╞══════╪══════╪═══════════╡
# │ -1 ┆ 1.0 ┆ 135.0 │
# │ 0.0 ┆ 1.0 ┆ 90.0 │
# │ 1.0 ┆ 0.0 ┆ 0.0 │
# │ 1.0 ┆ -1.0 ┆ -45.0 │
# └──────┴──────┴───────────┘
.. _cot:
COT
---
Compute the cotangent of the input column (in radians).
**Example:**
.. code-block:: python
df = pl.DataFrame({"rads": [-2.0, -1.0, 0.0, 1.0, 2.0]})
df.sql("SELECT rads, COT(rads) AS cot FROM self")
# shape: (5, 2)
# ┌──────┬───────────┐
# │ rads ┆ cot │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪═══════════╡
# │ -2.0 ┆ 0.457658 │
# │ -1.0 ┆ -0.642093 │
# │ 0.0 ┆ inf │
# │ 1.0 ┆ 0.642093 │
# │ 2.0 ┆ -0.457658 │
# └──────┴───────────┘
.. _cotd:
COTD
----
Compute cotangent of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [0, 90, 180, 270, 360]})
df.sql("SELECT degs, COTD(degs) AS cotd FROM self")
# shape: (5, 2)
# ┌──────┬────────────┐
# │ degs ┆ cotd │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪════════════╡
# │ -2.0 ┆ -28.636253 │
# │ -1.0 ┆ -57.289962 │
# │ 0.0 ┆ inf │
# │ 1.0 ┆ 57.289962 │
# │ 2.0 ┆ 28.636253 │
# └──────┴────────────┘
.. _cos:
COS
---
Compute the cosine of the input column (in radians).
**Example:**
.. code-block:: python
df = pl.DataFrame({"rads": [-2.0, -1.0, 0.0, 1.0, 2.0]})
df.sql("SELECT rads, COS(rads) AS cos FROM self")
# shape: (5, 2)
# ┌──────┬───────────┐
# │ rads ┆ cos │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════╪═══════════╡
# │ -2.0 ┆ -0.416147 │
# │ -1.0 ┆ 0.540302 │
# │ 0.0 ┆ 1.0 │
# │ 1.0 ┆ 0.540302 │
# │ 2.0 ┆ -0.416147 │
# └──────┴───────────┘
.. _cosd:
COSD
----
Compute the cosine of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [0, 45, 180, 225]})
df.sql("SELECT degs, COSD(degs) AS cosd FROM self")
# shape: (4, 2)
# ┌──────┬───────────┐
# │ degs ┆ cosd │
# │ --- ┆ --- │
# │ i64 ┆ f64 │
# ╞══════╪═══════════╡
# │ 0 ┆ 1.0 │
# │ 45 ┆ 0.707107 │
# │ 180 ┆ -1.0 │
# │ 225 ┆ -0.707107 │
# └──────┴───────────┘
.. _degrees:
DEGREES
-------
Convert between radians and degrees.
**Example:**
.. code-block:: python
import math
df = pl.DataFrame({"rads": [0.0, math.pi/2, math.pi, 3*math.pi/2]})
df.sql("SELECT rads, DEGREES(rads) AS degs FROM self")
# shape: (4, 2)
# ┌──────────┬───────┐
# │ rads ┆ degs │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════════╪═══════╡
# │ 0.0 ┆ 0.0 │
# │ 1.570796 ┆ 90.0 │
# │ 3.141593 ┆ 180.0 │
# │ 4.712389 ┆ 270.0 │
# └──────────┴───────┘
.. _radians:
RADIANS
-------
Convert between degrees and radians.
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [0, 90, 180, 270]})
df.sql("SELECT degs, RADIANS(degs) AS rads FROM self")
# shape: (4, 2)
# ┌──────┬──────────┐
# │ degs ┆ rads │
# │ --- ┆ --- │
# │ i64 ┆ f64 │
# ╞══════╪══════════╡
# │ 0 ┆ 0.0 │
# │ 90 ┆ 1.570796 │
# │ 180 ┆ 3.141593 │
# │ 270 ┆ 4.712389 │
# └──────┴──────────┘
.. _sin:
SIN
---
Compute the sine of the input column (in radians).
**Example:**
.. code-block:: python
import math
df = pl.DataFrame({"rads": [0.0, 1/4 * math.pi, 1/2 * math.pi, 3/4 * math.pi]})
df.sql("SELECT rads, SIN(rads) AS sin FROM self")
# shape: (4, 2)
# ┌──────────┬──────────┐
# │ rads ┆ sin │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════════╪══════════╡
# │ 0.0 ┆ 0.0 │
# │ 0.785398 ┆ 0.707107 │
# │ 1.570796 ┆ 1.0 │
# │ 2.356194 ┆ 0.707107 │
# └──────────┴──────────┘
.. _sind:
SIND
----
Compute the sine of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [0, 90, 225, 270]})
df.sql("SELECT degs, SIND(degs) AS sind FROM self")
# shape: (4, 2)
# ┌──────┬───────────┐
# │ degs ┆ sind │
# │ --- ┆ --- │
# │ i64 ┆ f64 │
# ╞══════╪═══════════╡
# │ 0 ┆ 0.0 │
# │ 90 ┆ 1.0 │
# │ 225 ┆ -0.707107 │
# │ 270 ┆ -1.0 │
# └──────┴───────────┘
.. _tan:
TAN
---
Compute the tangent of the input column (in radians).
**Example:**
.. code-block:: python
import math
df = pl.DataFrame({"rads": [0.0, 1/4 * math.pi, 3/4 * math.pi]})
df.sql("SELECT rads, TAN(rads) AS tan FROM self")
# shape: (4, 2)
# ┌──────────┬───────────┐
# │ rads ┆ tan │
# │ --- ┆ --- │
# │ f64 ┆ f64 │
# ╞══════════╪═══════════╡
# │ 0.0 ┆ 0.0 │
# │ 0.785398 ┆ 1.0 │
# │ 1.570796 ┆ 1.6331e16 │
# │ 2.356194 ┆ -1.0 │
# └──────────┴───────────┘
.. _tand:
TAND
----
Compute the tangent of the input column (in degrees).
**Example:**
.. code-block:: python
df = pl.DataFrame({"degs": [0, 45, 135, 225]})
df.sql("SELECT degs, TAND(degs) AS tand FROM self")
# shape: (4, 2)
# ┌──────┬──────┐
# │ degs ┆ tand │
# │ --- ┆ --- │
# │ i64 ┆ f64 │
# ╞══════╪══════╡
# │ 0 ┆ 0.0 │
# │ 45 ┆ 1.0 │
# │ 135 ┆ -1.0 │
# │ 225 ┆ 1.0 │
# └──────┴──────┘