Trigonometric Functions HelixQL provides a comprehensive set of trigonometric functions for angular calculations, including standard trigonometric functions (sine, cosine, tangent) and their inverse counterparts, essential for geospatial calculations, physics simulations, and angular measurements.
Available Functions SIN - Sine Returns the sine of an angle in radians.
COS - Cosine Returns the cosine of an angle in radians.
TAN - Tangent Returns the tangent of an angle in radians.
ASIN - Arcsine ASIN ( x ) // Returns arcsin(x) Returns the arcsine (inverse sine) of x in radians. Domain: [-1, 1].
ACOS - Arccosine ACOS ( x ) // Returns arccos(x) Returns the arccosine (inverse cosine) of x in radians. Domain: [-1, 1].
ATAN - Arctangent ATAN ( x ) // Returns arctan(x) Returns the arctangent (inverse tangent) of x in radians.
ATAN2 - Two-Argument Arctangent ATAN2 ( y , x ) // Returns atan2(y, x) Returns the angle in radians between the positive x-axis and the point (x, y). This function handles all quadrants correctly and is commonly used for angle calculations.
When using the SDKs or curling the endpoint, the query name must match what is defined in the queries.hx file exactly.
Example 1: Geospatial bearing calculations Calculate the bearing (direction) between geographic coordinates:
QUERY CalculateBearings () => locations <- N :: Location :: { name , latitude , longitude , radians_lat : MUL ( _ :: { latitude }, DIV ( PI (), 180.0 )), radians_lon : MUL ( _ :: { longitude }, DIV ( PI (), 180.0 )), sin_lat : SIN ( MUL ( _ :: { latitude }, DIV ( PI (), 180.0 ))), cos_lat : COS ( MUL ( _ :: { latitude }, DIV ( PI (), 180.0 ))), tan_lat : TAN ( MUL ( _ :: { latitude }, DIV ( PI (), 180.0 ))) } RETURN locations QUERY CreateLocation ( name : String , latitude : F64 , longitude : F64 ) => location <- AddN < Location >({ name : name , latitude : latitude , longitude : longitude }) RETURN location
Here’s how to run the query using the SDKs or curl
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Rust
Go
TypeScript
Curl
from helix.client import Client client = Client( local = True , port = 6969 ) # Create locations with geographic coordinates locations = [ { "name" : "New York" , "latitude" : 40.7128 , "longitude" : - 74.0060 }, { "name" : "London" , "latitude" : 51.5074 , "longitude" : - 0.1278 }, { "name" : "Tokyo" , "latitude" : 35.6762 , "longitude" : 139.6503 }, ] for location in locations: client.query( "CreateLocation" , location) result = client.query( "CalculateBearings" , {}) print ( "Location bearings:" , result)
Example 2: Angle calculations with ATAN2 Use ATAN2 to calculate angles between vectors and points:
QUERY CalculateAngles () => vectors <- N :: Vector :: { x , y , angle_radians : ATAN2 ( _ :: { y }, _ :: { x }), angle_degrees : MUL ( ATAN2 ( _ :: { y }, _ :: { x }), DIV ( 180.0 , PI ())) } RETURN vectors QUERY CreateVector ( x : F64 , y : F64 ) => vector <- AddN < Vector >({ x : x , y : y }) RETURN vector
Here’s how to run the query using the SDKs or curl
Python
Rust
Go
TypeScript
Curl
from helix.client import Client client = Client( local = True , port = 6969 ) # Create vectors in different quadrants vectors = [ { "x" : 1.0 , "y" : 1.0 }, # 45 degrees { "x" : - 1.0 , "y" : 1.0 }, # 135 degrees { "x" : - 1.0 , "y" : - 1.0 }, # -135 degrees { "x" : 1.0 , "y" : - 1.0 }, # -45 degrees ] for vector in vectors: client.query( "CreateVector" , vector) result = client.query( "CalculateAngles" , {}) print ( "Vector angles:" , result)
Example 3: Inverse trigonometric functions Use inverse trigonometric functions to recover angles from ratios:
QUERY RecoverAngles () => measurements <- N :: Measurement :: { ratio , angle_from_sin : ASIN ( _ :: { ratio }), angle_from_cos : ACOS ( _ :: { ratio }), angle_from_tan : ATAN ( _ :: { ratio }) } RETURN measurements QUERY CreateMeasurement ( ratio : F64 ) => measurement <- AddN < Measurement >({ ratio : ratio }) RETURN measurement
Here’s how to run the query using the SDKs or curl
Python
Rust
Go
TypeScript
Curl
from helix.client import Client client = Client( local = True , port = 6969 ) # Create measurements with various ratios ratios = [ 0.0 , 0.5 , 0.707 , 0.866 , 1.0 ] for ratio in ratios: client.query( "CreateMeasurement" , { "ratio" : ratio}) result = client.query( "RecoverAngles" , {}) print ( "Recovered angles:" , result)
Radians vs Degrees All trigonometric functions in HelixQL work with radians. To convert between degrees and radians:
// Degrees to radians radians = MUL ( degrees , DIV ( PI (), 180.0 )) // Radians to degrees degrees = MUL ( radians , DIV ( 180.0 , PI ())) Use the PI() constant function for accurate conversion between degrees and radians.
Domain Restrictions Inverse trigonometric functions have domain restrictions:
ASIN(x), ACOS(x) : x must be in [-1, 1]ATAN(x) : accepts all real numbersATAN2(y, x) : accepts all real numbers for both arguments ATAN2 vs ATAN ATAN2 is preferred over ATAN for angle calculations because:
It handles all four quadrants correctly
It avoids division by zero when x = 0
It returns values in the full range [-π, π]
// ATAN2 correctly handles all quadrants ATAN2 ( 1.0 , 1.0 ) // π/4 (first quadrant) ATAN2 ( 1.0 , - 1.0 ) // 3π/4 (second quadrant) ATAN2 ( - 1.0 , - 1.0 ) // -3π/4 (third quadrant) ATAN2 ( - 1.0 , 1.0 ) // -π/4 (fourth quadrant) Use in Geospatial Calculations Trigonometric functions are essential for geospatial calculations:
// Calculate great circle distance (Haversine formula) QUERY CalculateDistance ( lat1 : F64 , lon1 : F64 , lat2 : F64 , lon2 : F64 ) => dlat <- SUB ( lat2 , lat1 ) dlon <- SUB ( lon2 , lon1 ) a <- ADD ( POW ( SIN ( DIV ( dlat , 2.0 )), 2.0 ), MUL ( MUL ( COS ( lat1 ), COS ( lat2 )), POW ( SIN ( DIV ( dlon , 2.0 )), 2.0 )) ) c <- MUL ( 2.0 , ATAN2 ( SQRT ( a ), SQRT ( SUB ( 1.0 , a )))) distance <- MUL ( 6371.0 , c ) // Earth radius in km RETURN distance Unary Math Functions SQRT, ABS, LN, LOG10, EXP, CEIL, FLOOR, ROUND
Constants PI and E constants
Arithmetic Functions ADD, SUB, MUL, DIV, POW, MOD
Math Overview Overview of all math functions
