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       │
# ╞══════╪══════╪═══════════╡
# │ -1.0 ┆ 1.0  ┆ -45.0     │
# │ 0.0  ┆ 1.0  ┆ 0.0       │
# │ 1.0  ┆ 0.0  ┆ 90.0      │
# │ 1.0  ┆ -1.0 ┆ 135.0     │
# └──────┴──────┴───────────┘

.. _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": [30, 45, 60]})
df.sql("SELECT degs, COTD(degs) AS cotd FROM self")
# shape: (3, 2)
# ┌──────┬──────────┐
# │ degs ┆ cotd     │
# │ ---  ┆ ---      │
# │ i64  ┆ f64      │
# ╞══════╪══════════╡
# │ 30   ┆ 1.732051 │
# │ 45   ┆ 1.0      │
# │ 60   ┆ 0.57735  │
# └──────┴──────────┘

.. _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       │
# │ 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  │
# └──────┴──────┘