---
title: "cos"
slug: "dev-database-reference-sql-functions-numeric-cos"
updated: 2026-10-30T18:18:51Z
published: 2026-10-30T18:18:51Z
canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-cos"
---

> ## Documentation Index
> Fetch the complete documentation index at: https://docs.vastdata.com/llms.txt
> Use this file to discover all available pages before exploring further.

# cos

*Applies to VAST Cluster 5.5.*

*[Functions](/develop/docs/dev-database-reference-sql-functions-index) › [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric) › Trigonometry.* Returns the cosine of an angle given in radians, from -1 to 1. For an angle in degrees, convert it first with [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians): `cos(radians(deg))`. It has no aliases.

## Syntax

```
cos(x)
```

| Argument | Type | Description |
| --- | --- | --- |
| `x` | `DOUBLE` (any integer, `DECIMAL` or `FLOAT` is converted) | The angle, in radians. |

**Returns:** `DOUBLE`, from -1 to 1.

**Aliases:** none.

## Set up the examples

The examples connect with the ADBC driver, as in [VAST Query Engine (ADBC)](/develop/docs/dev-database-integrations-adbc), and work in a schema called `docs_sql_fn_numeric_cos`. Set `QE_ENDPOINT`, `AWS_ACCESS_KEY_ID`, `AWS_SECRET_ACCESS_KEY` and `VASTDB_BUCKET` ([SQL reference](/develop/docs/dev-database-reference-sql-index#example-connect-and-use-a-transaction)), and run the blocks in order in one Python session. Below each block is the output you should see.

This block connects, defines the `run()` and `plan()` helpers, and creates a table of the five segments of a robot arm, each with its length in metres and its angle in radians. The last row has no values:

```
import os
import re

import adbc_driver_manager
import adbc_driver_manager.dbapi as dbapi
import adbc_driver_vastdb

BUCKET = os.environ["VASTDB_BUCKET"]
SCHEMA = f'"{BUCKET}/docs_sql_fn_numeric_cos"'

conn = dbapi.connect(
    driver=adbc_driver_vastdb.get_driver_path(),
    db_kwargs={
        "vast.db.endpoint": os.environ["QE_ENDPOINT"],
        "vast.db.access_key": os.environ["AWS_ACCESS_KEY_ID"],
        "vast.db.secret_key": os.environ["AWS_SECRET_ACCESS_KEY"],
    },
    autocommit=True,
)

def server_message(e):
    """The server's message in a driver error, without the request ID or the echoed statement."""
    text = re.sub(r"\[req=0x[0-9a-f]+\]: ", "", str(e))
    found = (re.search(r'message: "(.*?)", request_id', text, re.S)
             or re.search(r"description: (.*)\)", text, re.S))
    message = found.group(1) if found else text.strip().splitlines()[-1]
    message = re.sub(r"^Plan query: '.*?' failed with: ", "", message, flags=re.S)
    message = re.split(r"\\n|\n", message)[0].replace('\\"', '"')
    return message.replace(BUCKET, "<bucket>")

def run(sql):
    """Run one statement. Print the rows it returns, or the error."""
    try:
        with conn.cursor() as cur:
            cur.execute(sql)
            rows = cur.fetchall() if cur.description else []
    except (adbc_driver_manager.Error, OSError) as e:
        print(f"{type(e).__name__}: {server_message(e)}")
    else:
        print(rows)

def plan(sql):
    """Print the plan without its ~N Rows lines: the table's row count, which can still be 0 just after an insert."""
    with conn.cursor() as cur:
        cur.execute("EXPLAIN " + sql)
        steps = cur.fetchall()[0][1]
    print("\n".join(line for line in steps.splitlines() if "Rows" not in line))

TABLE = f"{SCHEMA}.joints"
run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}")
run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, joint VARCHAR, len DOUBLE, angle DOUBLE)")
run(f"INSERT INTO {TABLE} VALUES "
    "(1, 'shoulder', 0.5, 1.0), "
    "(2, 'elbow', 0.4, 2.5), "
    "(3, 'wrist', 0.2, -1.25), "
    "(4, 'gripper', 0.1, 0.0), "
    "(5, NULL, NULL, NULL)")
```

```
[]
[]
[(5,)]
```

## What it does

`cos(x)` returns the cosine of the angle `x`, in radians: `cos(0)` is `1.0` and `cos(pi())` is `-1.0`. The cosine is the same for `x` and `-x`, so `cos(-0.0::DOUBLE)` is `1.0` too. The argument is converted to `DOUBLE`, and so is the result, whatever the argument's type. A string of digits is converted too: `cos(&apos;12&apos;)` returns `0.8438539587324921`.

[pi](/develop/docs/dev-database-reference-sql-functions-numeric-pi)`()` is π rounded to a `DOUBLE`, so an angle built from it isn't exact, and neither is its cosine: `cos(pi() / 2)` is `6.123233995736766e-17`, not 0, and `cos(pi() / 3)` is `0.5000000000000001`, not 0.5. Compare results with a tolerance, such as `abs(cos(x)) &lt; 1e-9`, rather than with `=`.

Any finite angle works, however large: `cos(1e308)` returns `-0.8913089376870335`. An infinite angle is an error, and `nan` gives `nan`.

## NULLs and edge cases

| Input | Result |
| --- | --- |
| `NULL` | `NULL` |
| `0`, `-0.0::DOUBLE` | `1.0` |
| `pi() / 3` | `0.5000000000000001` |
| `pi() / 2` | `6.123233995736766e-17` |
| `pi()` | `-1.0` |
| `5e-324::DOUBLE` (the smallest `DOUBLE` above 0) | `1.0` |
| `1e308` | `-0.8913089376870335` |
| `&apos;nan&apos;::DOUBLE` | `nan` |
| `&apos;12&apos;` (a string of digits) | `0.8438539587324921` |
| `&apos;inf&apos;::DOUBLE` | Error: `input value inf is out of range for numeric function` |
| `&apos;-inf&apos;::DOUBLE` | Error: `input value -inf is out of range for numeric function` |
| `&apos;abc&apos;` | Error: `Could not convert string &apos;abc&apos; to DOUBLE` |
| A `BLOB`, date, boolean, list or interval | Error: `No function matches the given name and argument types`, for example `&apos;cos(DATE)&apos;` |

The same cases, as the cluster returns them. They use the helpers from [Set up the examples](/develop/docs/dev-database-reference-sql-functions-numeric-cos#set-up-the-examples):

```
run("SELECT cos(NULL), cos(0), cos(-0.0::DOUBLE), cos(pi() / 3), cos(pi() / 2), cos(pi())")
run("SELECT cos(5e-324::DOUBLE), cos(1e308), cos('nan'::DOUBLE)")
run("SELECT cos('12')")
run("SELECT cos('inf'::DOUBLE)")
run("SELECT cos('-inf'::DOUBLE)")
run("SELECT cos('abc')")
run("SELECT cos('\\xAA'::BLOB)")
run("SELECT cos(DATE '2026-10-16')")
run("SELECT cos(true)")
run("SELECT cos([1, 2])")
run("SELECT cos(INTERVAL 1 DAY)")
```

```
[(None, 1.0, 1.0, 0.5000000000000001, 6.123233995736766e-17, -1.0)]
[(1.0, -0.8913089376870335, nan)]
[(0.8438539587324921,)]
OSError: input value inf is out of range for numeric function
OSError: input value -inf is out of range for numeric function
OSError: Could not convert string 'abc' to DOUBLE
InternalError: Binder Error: No function matches the given name and argument types 'cos(BLOB)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'cos(DATE)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'cos(BOOLEAN)'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'cos(INTEGER[])'. You might need to add explicit type casts.
InternalError: Binder Error: No function matches the given name and argument types 'cos(INTERVAL)'. You might need to add explicit type casts.
```

## Examples

The cosine of each joint's angle, and the horizontal reach of each segment, its length times the cosine of its angle:

```
run(f"SELECT id, joint, cos(angle), len * cos(angle) FROM {TABLE} ORDER BY id LIMIT 10")
```

```
[(1, 'shoulder', 0.5403023058681398, 0.2701511529340699), (2, 'elbow', -0.8011436155469337, -0.3204574462187735), (3, 'wrist', 0.3153223623952687, 0.06306447247905374), (4, 'gripper', 1.0, 0.1), (5, None, None, None)]
```

An angle in degrees, converted with [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians) first:

```
run("SELECT cos(radians(60)), cos(radians(180))")
```

```
[(0.5000000000000001, -1.0)]
```

Keep only the segments that point forwards:

```
run(f"SELECT id, joint FROM {TABLE} WHERE cos(angle) > 0 ORDER BY id LIMIT 10")
```

```
[(1, 'shoulder'), (3, 'wrist'), (4, 'gripper')]
```

## How it runs in VAST

The Query Engine runs on the cluster's CNodes, and a query on a table starts with a scan in VAST DataBase (`VAST_SCAN`). VAST DataBase can evaluate a comparison of a column with a constant, but not a function of a column, so `cos()` is always computed by the Query Engine:

- **In the `SELECT` list,** the scan reads the column and the Query Engine computes `cos()` for each row it returns.
- **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `cos()` and keeps the rows that match. No rows are skipped in storage.

The plan of the `WHERE` example shows the `FILTER` step above the scan:

```
plan(f"SELECT id FROM {TABLE} WHERE cos(angle) > 0")
```

```
┌───────────────────────────┐
│         PROJECTION        │
│    ────────────────────   │
│             #1            │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│           FILTER          │
│    ────────────────────   │
│     (cos(angle) > 0.0)    │
│                           │
└─────────────┬─────────────┘
┌─────────────┴─────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│                           │
│        Projections:       │
│           angle           │
│             id            │
│                           │
└───────────────────────────┘
```

## Make it faster

- **Convert the constant, not the column.** A function of constants is computed once, and the comparison is pushed down to VAST DataBase, so rows that don't match never leave storage. If your angles lie in a known range, write the condition on the angle itself: for angles from -π to π, `cos(angle) &gt; 0` is `angle &gt; -pi() / 2 AND angle &lt; pi() / 2`. The plan for a comparison with `pi() / 2` has no `FILTER` step:

```
plan(f"SELECT id FROM {TABLE} WHERE angle < pi() / 2")
```

```
┌───────────────────────────┐
│         VAST_SCAN         │
│    ────────────────────   │
│    Function: VAST_SCAN    │
│      Projections: id      │
│                           │
└───────────────────────────┘
```

- **Store the cosine if you filter on it often.** Compute it when you write the rows and keep it in its own column: a comparison of that column is pushed down, `cos(angle)` in `WHERE` isn't.
- **Combine it with a pushed-down condition.** In `id &gt; 100 AND cos(angle) &gt; 0`, `id &gt; 100` is still evaluated in VAST DataBase, so `cos()` runs only on the rows that pass it.

## Limitations and errors

- **Radians only.** There is no degree version: `cosd` fails with `Scalar Function with name cosd does not exist!`. Use `cos(radians(x))`.
- **No `sec`.** For the secant, use `1 / cos(x)`.
- **Infinite angles are errors.** `cos(&apos;inf&apos;::DOUBLE)` fails with `input value inf is out of range for numeric function`, and `&apos;-inf&apos;::DOUBLE` with the same message for `-inf`. Test for them with [isinf](/develop/docs/dev-database-reference-sql-functions-numeric-isinf) or [isfinite](/develop/docs/dev-database-reference-sql-functions-numeric-isfinite).
- **One argument, numbers only.** `cos(1, 2)`, a `BLOB`, a date, a boolean, a list or an interval fails with `No function matches the given name and argument types`. A string is converted to `DOUBLE`, so a string that isn't a number fails with `Could not convert string ... to DOUBLE`.

```
run("SELECT cosd(60)")
run("SELECT sec(0)")
run("SELECT cos(1, 2)")
```

```
InternalError: Catalog Error: Scalar Function with name cosd does not exist!
InternalError: Catalog Error: Scalar Function with name sec does not exist!
InternalError: Binder Error: No function matches the given name and argument types 'cos(INTEGER_LITERAL, INTEGER_LITERAL)'. You might need to add explicit type casts.
```

## Similar functions

| Function | Computes | Result for `pi() / 4` |
| --- | --- | --- |
| `cos(x)` | the cosine | `0.7071067811865476` |
| [sin](/develop/docs/dev-database-reference-sql-functions-numeric-sin) | the sine | `0.7071067811865475` |
| [tan](/develop/docs/dev-database-reference-sql-functions-numeric-tan) | the tangent, `sin(x) / cos(x)` | `0.9999999999999999` |
| [cot](/develop/docs/dev-database-reference-sql-functions-numeric-cot) | the cotangent, `cos(x) / sin(x)` | `1.0000000000000002` |
| [acos](/develop/docs/dev-database-reference-sql-functions-numeric-acos) | the inverse: the angle whose cosine is `x` |  |
| [cosh](/develop/docs/dev-database-reference-sql-functions-numeric-cosh) | the hyperbolic cosine |  |

```
run("SELECT cos(pi() / 4), sin(pi() / 4), tan(pi() / 4), cot(pi() / 4)")
```

```
[(0.7071067811865476, 0.7071067811865475, 0.9999999999999999, 1.0000000000000002)]
```

Clean up:

```
run(f"DROP TABLE IF EXISTS {TABLE}")
run(f"DROP SCHEMA IF EXISTS {SCHEMA}")
conn.close()
```

```
[]
[]
```

## See also

- [Numeric and math functions](/develop/docs/dev-database-reference-sql-functions-numeric#trigonometry): all the trigonometric functions.
- [sin](/develop/docs/dev-database-reference-sql-functions-numeric-sin), [tan](/develop/docs/dev-database-reference-sql-functions-numeric-tan), [acos](/develop/docs/dev-database-reference-sql-functions-numeric-acos), [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians) and [degrees](/develop/docs/dev-database-reference-sql-functions-numeric-degrees).
- [Where filters run](/develop/docs/dev-database-reference-sql-select#where-filters-run) and [pushdowns](/develop/docs/dev-database-reference-pushdowns).
- [EXPLAIN](/develop/docs/dev-database-reference-sql-explain): how to read a plan.