Trigonometry

ACOS	Compute inverse cosine of the input column (in radians).
ACOSD	Compute inverse cosine of the input column (in degrees).
ASIN	Compute inverse sine of the input column (in radians).
ASIND	Compute inverse sine of the input column (in degrees).
ATAN	Compute inverse tangent of the input column (in radians).
ATAND	Compute inverse tangent of the input column (in degrees).
ATAN2	Compute the inverse tangent of column_2/column_1 (in radians).
ATAN2D	Compute the inverse tangent of column_2/column_1 (in degrees).
COT	Compute the cotangent of the input column (in radians).
COTD	Compute cotangent of the input column (in degrees).
COS	Compute the cosine of the input column (in radians).
COSD	Compute the cosine of the input column (in degrees).
DEGREES	Convert between radians and degrees.
RADIANS	Convert between degrees and radians.
SIN	Compute the sine of the input column (in radians).
SIND	Compute the sine of the input column (in degrees).
TAN	Compute the tangent of the input column (in radians).
TAND	Compute the tangent of the input column (in degrees).

ACOS

Compute inverse cosine of the input column (in radians).

Example:

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

Compute inverse cosine of the input column (in degrees).

Example:

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

Compute inverse sine of the input column (in radians).

Example:

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

Compute inverse sine of the input column (in degrees).

Example:

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

Compute inverse tangent of the input column (in radians).

Example:

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

Compute inverse tangent of the input column (in degrees).

Example:

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

Compute the inverse tangent of column_2/column_1 (in radians).

Example:

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

Compute the inverse tangent of column_2/column_1 (in degrees).

Example:

df = pl.DataFrame(
    {
        "a": [0, 90, 180, 360],
        "b": [360, 270, 180, 90],
    }
)
df.sql("SELECT a, b, ATAN2D(a, b) AS atan2d_ab FROM self")
# shape: (4, 3)
# ┌─────┬─────┬───────────┐
# │ a   ┆ b   ┆ atan2d_ab │
# │ --- ┆ --- ┆ ---       │
# │ i64 ┆ i64 ┆ f64       │
# ╞═════╪═════╪═══════════╡
# │ 0   ┆ 360 ┆ 0.0       │
# │ 90  ┆ 270 ┆ 18.434949 │
# │ 180 ┆ 180 ┆ 45.0      │
# │ 360 ┆ 90  ┆ 75.963757 │
# └─────┴─────┴───────────┘

COT

Compute the cotangent of the input column (in radians).

Example:

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

Compute cotangent of the input column (in degrees).

Example:

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

Compute the cosine of the input column (in radians).

Example:

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

Compute the cosine of the input column (in degrees).

Example:

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

Convert between radians and degrees.

Example:

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

Convert between degrees and radians.

Example:

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

Compute the sine of the input column (in radians).

Example:

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

Compute the sine of the input column (in degrees).

Example:

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

Compute the tangent of the input column (in radians).

Example:

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

Compute the tangent of the input column (in degrees).

Example:

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  │
# └──────┴──────┘