--- title: "tan" slug: "dev-database-reference-sql-functions-numeric-tan" updated: 2026-10-30T18:18:51Z published: 2026-10-30T18:18:51Z canonical: "docs.vastdata.com/dev-database-reference-sql-functions-numeric-tan" --- > ## 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. # tan *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 tangent of an angle given in radians: `sin(x) / cos(x)`, the slope of a line at that angle. For an angle in degrees, convert it first with [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians): `tan(radians(deg))`. It has no aliases. ## Syntax ``` tan(x) ``` | Argument | Type | Description | | --- | --- | --- | | `x` | `DOUBLE` (any integer, `DECIMAL` or `FLOAT` is converted) | The angle, in radians. | **Returns:** `DOUBLE`. **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_tan`. 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 five ramps, each with its horizontal run in metres and its angle of incline 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_tan"' 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, "") 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}.ramps" run(f"CREATE SCHEMA IF NOT EXISTS {SCHEMA}") run(f"CREATE TABLE IF NOT EXISTS {TABLE} (id BIGINT, ramp VARCHAR, run_m DOUBLE, angle DOUBLE)") run(f"INSERT INTO {TABLE} VALUES " "(1, 'loading dock', 4.0, 0.1), " "(2, 'garage', 6.0, 0.25), " "(3, 'stair lift', 2.0, 1.0), " "(4, 'corridor', 10.0, 0.0), " "(5, NULL, NULL, NULL)") ``` ``` [] [] [(5,)] ``` ## What it does `tan(x)` returns the tangent of the angle `x`, in radians: `tan(0)` is `0.0`, and `tan(1)` is `1.5574077246549023`. It repeats every π, and changes sign with `x`. The argument is converted to `DOUBLE`, and so is the result, whatever the argument's type. A string of digits is converted too: `tan('12')` returns `-0.6358599286615808`. [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 tangent: `tan(pi() / 4)` is `0.9999999999999999`, not 1, and `tan(pi())` is `-1.2246467991473532e-16`, not 0. At π/2 the tangent isn't defined, but `pi() / 2` isn't exactly π/2, so `tan(pi() / 2)` returns a large finite number, `1.633123935319537e+16`, rather than `inf` or an error. An infinite angle is an error, and `nan` gives `nan`. ## NULLs and edge cases | Input | Result | | --- | --- | | `NULL` | `NULL` | | `0` | `0.0` | | `-0.0::DOUBLE` | `-0.0` | | `pi() / 4` | `0.9999999999999999` | | `pi() / 2` | `1.633123935319537e+16` | | `-pi() / 2` | `-1.633123935319537e+16` | | `pi()` | `-1.2246467991473532e-16` | | `5e-324::DOUBLE` (the smallest `DOUBLE` above 0) | `5e-324` | | `'nan'::DOUBLE` | `nan` | | `'12'` (a string of digits) | `-0.6358599286615808` | | `'inf'::DOUBLE` | Error: `input value inf is out of range for numeric function` | | `'-inf'::DOUBLE` | Error: `input value -inf is out of range for numeric function` | | `'abc'` | Error: `Could not convert string 'abc' to DOUBLE` | | A `BLOB`, date, boolean, list or interval | Error: `No function matches the given name and argument types`, for example `'tan(DATE)'` | 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-tan#set-up-the-examples): ``` run("SELECT tan(NULL), tan(0), tan(-0.0::DOUBLE), tan(pi() / 4), tan(pi() / 2), tan(-pi() / 2), tan(pi())") run("SELECT tan(5e-324::DOUBLE), tan('nan'::DOUBLE)") run("SELECT tan('12')") run("SELECT tan('inf'::DOUBLE)") run("SELECT tan('-inf'::DOUBLE)") run("SELECT tan('abc')") run("SELECT tan('\\xAA'::BLOB)") run("SELECT tan(DATE '2026-10-16')") run("SELECT tan(true)") run("SELECT tan([1, 2])") run("SELECT tan(INTERVAL 1 DAY)") ``` ``` [(None, 0.0, -0.0, 0.9999999999999999, 1.633123935319537e+16, -1.633123935319537e+16, -1.2246467991473532e-16)] [(5e-324, nan)] [(-0.6358599286615808,)] 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 'tan(BLOB)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'tan(DATE)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'tan(BOOLEAN)'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'tan(INTEGER[])'. You might need to add explicit type casts. InternalError: Binder Error: No function matches the given name and argument types 'tan(INTERVAL)'. You might need to add explicit type casts. ``` ## Examples The slope of each ramp, the tangent of its angle, and the height it climbs over its run: ``` run(f"SELECT id, ramp, tan(angle), run_m * tan(angle) FROM {TABLE} ORDER BY id LIMIT 10") ``` ``` [(1, 'loading dock', 0.10033467208545055, 0.4013386883418022), (2, 'garage', 0.25534192122103627, 1.5320515273262176), (3, 'stair lift', 1.5574077246549023, 3.1148154493098046), (4, 'corridor', 0.0, 0.0), (5, None, None, None)] ``` A slope given in degrees, converted with [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians) first: ``` run("SELECT tan(radians(45)), tan(radians(5))") ``` ``` [(0.9999999999999999, 0.08748866352592401)] ``` Keep only the ramps steeper than a 1 in 5 slope: ``` run(f"SELECT id, ramp FROM {TABLE} WHERE tan(angle) > 0.2 ORDER BY id LIMIT 10") ``` ``` [(2, 'garage'), (3, 'stair lift')] ``` ## 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 `tan()` is always computed by the Query Engine: - **In the `SELECT` list,** the scan reads the column and the Query Engine computes `tan()` for each row it returns. - **In `WHERE`,** the scan sends the column for every row, and a `FILTER` step in the Query Engine computes `tan()` 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 tan(angle) > 0.2") ``` ``` ┌───────────────────────────┐ │ PROJECTION │ │ ──────────────────── │ │ #1 │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ FILTER │ │ ──────────────────── │ │ (tan(angle) > 0.2) │ │ │ └─────────────┬─────────────┘ ┌─────────────┴─────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ │ │ Projections: │ │ angle │ │ id │ │ │ └───────────────────────────┘ ``` ## Make it faster - **Compare the angle, not its tangent.** Between -π/2 and π/2 the tangent grows with the angle, so for angles in that range `tan(angle) > 1` keeps the same rows as `angle > pi() / 4`, up to rounding at the boundary itself. A function of constants is computed once, and the comparison of the raw column is pushed down to VAST DataBase, so rows that don't match never leave storage. The plan has no `FILTER` step: ``` plan(f"SELECT id FROM {TABLE} WHERE angle > pi() / 4") ``` ``` ┌───────────────────────────┐ │ VAST_SCAN │ │ ──────────────────── │ │ Function: VAST_SCAN │ │ Projections: id │ │ │ └───────────────────────────┘ ``` - **Store the slope 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, `tan(angle)` in `WHERE` isn't. - **Combine it with a pushed-down condition.** In `id > 100 AND tan(angle) > 0.2`, `id > 100` is still evaluated in VAST DataBase, so `tan()` runs only on the rows that pass it. ## Limitations and errors - **Radians only.** Convert degrees with [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians): `tan(radians(x))`. - **No error or `inf` at π/2.** Near an odd multiple of π/2, `tan()` returns a very large number, positive or negative. If such angles can occur, test the angle rather than the result. - **Infinite angles are errors.** `tan('inf'::DOUBLE)` fails with `input value inf is out of range for numeric function`, and `'-inf'::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.** `tan(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`. For the angle of a point (x, y), with the right quadrant, use [atan2](/develop/docs/dev-database-reference-sql-functions-numeric-atan2). ``` run("SELECT tan(pi() / 2), tan(-pi() / 2)") run("SELECT tan(1, 2)") ``` ``` [(1.633123935319537e+16, -1.633123935319537e+16)] InternalError: Binder Error: No function matches the given name and argument types 'tan(INTEGER_LITERAL, INTEGER_LITERAL)'. You might need to add explicit type casts. ``` ## Similar functions | Function | Computes | Result for `pi() / 4` | | --- | --- | --- | | `tan(x)` | the tangent | `0.9999999999999999` | | [cot](/develop/docs/dev-database-reference-sql-functions-numeric-cot) | the cotangent, `1 / tan(x)` | `1.0000000000000002` | | `1 / tan(x)` | the cotangent, from `tan` | `1.0000000000000002` | | [sin](/develop/docs/dev-database-reference-sql-functions-numeric-sin), [cos](/develop/docs/dev-database-reference-sql-functions-numeric-cos) | the sine and cosine; `tan(x)` is `sin(x) / cos(x)` | `0.7071067811865475`, `0.7071067811865476` | | [atan](/develop/docs/dev-database-reference-sql-functions-numeric-atan) | the inverse: the angle whose tangent is `x` | | | [tanh](/develop/docs/dev-database-reference-sql-functions-numeric-tanh) | the hyperbolic tangent | | ``` run("SELECT tan(pi() / 4), cot(pi() / 4), 1 / tan(pi() / 4), sin(pi() / 4), cos(pi() / 4)") ``` ``` [(0.9999999999999999, 1.0000000000000002, 1.0000000000000002, 0.7071067811865475, 0.7071067811865476)] ``` 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), [cos](/develop/docs/dev-database-reference-sql-functions-numeric-cos), [cot](/develop/docs/dev-database-reference-sql-functions-numeric-cot), [atan](/develop/docs/dev-database-reference-sql-functions-numeric-atan) and [radians](/develop/docs/dev-database-reference-sql-functions-numeric-radians). - [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.