Mathematical functions - trigonometric

acos()

Details
Syntax	`acos(input)`
Description	Returns the arccosine of a `FLOAT` in radians.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`acos(null)` returns `null`.
If (`input` < -1) or (`input` > 1), then (`acos(input)`) returns `NaN`.

Example 1. acos()

Query

RETURN acos(0.5)

The arccosine of 0.5 is returned.

Result
acos(0.5)
`1.0471975511965979`
Rows: 1

asin()

Details
Syntax	`asin(input)`
Description	Returns the arcsine of a `FLOAT` in radians.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`asin(null)` returns `null`.
If (`input` < -1) or (`input` > 1), then (`asin(input)`) returns `NaN`.

Example 2. asin()

Query

RETURN asin(0.5)

The arcsine of 0.5 is returned.

Result
asin(0.5)
`0.5235987755982989`
Rows: 1

atan()

Details
Syntax	`atan(input)`
Description	Returns the arctangent of a `FLOAT` in radians.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`atan(null)` returns `null`.

Example 3. atan()

Query

RETURN atan(0.5)

The arctangent of 0.5 is returned.

Result
atan(0.5)
`0.4636476090008061`
Rows: 1

atan2()

Details
Syntax	`atan2(y, x)`
Description	Returns the arctangent2 of a set of coordinates in radians.
Arguments	Name	Type	Description
	`y`	`FLOAT`	A y angle in radians.
	`x`	`FLOAT`	An x angle in radians.
Returns	`FLOAT`

Considerations
`atan2(null, null)`, `atan2(null, x)` and `atan(y, null)` all return `null`.

Example 4. atan2()

Query

RETURN atan2(0.5, 0.6)

The arctangent2 of 0.5 and 0.6 is returned.

Result
atan2(0.5, 0.6)
`0.6947382761967033`
Rows: 1

cos()

Details
Syntax	`acos(input)`
Description	Returns the arccosine of a `FLOAT` in radians.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`cos(null)` returns `null`.

Example 5. cos()

Query

RETURN cos(0.5)

The cosine of 0.5 is returned.

Result
cos(0.5)
`0.8775825618903728`
Rows: 1

cot()

Details
Syntax	`cot(input)`
Description	Returns the cotangent of a `FLOAT`.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`cot(null)` returns `null`.
`cot(0)` returns `Infinity`.

Example 6. cot()

Query

RETURN cot(0.5)

The cotangent of 0.5 is returned.

Result
cot(0.5)
`1.830487721712452`
Rows: 1

degrees()

Details
Syntax	`degrees(input)`
Description	Converts radians to degrees.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`degrees(null)` returns `null`.

Example 7. degrees

Query

RETURN degrees(3.14159)

The number of degrees in something close to pi is returned.

Result
degrees(3.14159)
`179.9998479605043`
Rows: 1

haversin()

Details
Syntax	`haversin(input)`
Description	Returns half the versine of a number.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`haversin(null)` returns `null`.

Example 8. haversin()

Query

RETURN haversin(0.5)

The haversine of 0.5 is returned.

Result
haversin(0.5)
`0.06120871905481362`
Rows: 1

Spherical distance using the `haversin()` function

The haversin() function may be used to compute the distance on the surface of a sphere between two points (each given by their latitude and longitude).

Example 9. haversin()

In this example the spherical distance (in km) between Berlin in Germany (at lat 52.5, lon 13.4) and San Mateo in California (at lat 37.5, lon -122.3) is calculated using an average earth radius of 6371 km.

Query

CREATE (ber:City {lat: 52.5, lon: 13.4}), (sm:City {lat: 37.5, lon: -122.3})
RETURN 2 * 6371 * asin(sqrt(haversin(radians( sm.lat - ber.lat ))
  + cos(radians( sm.lat )) * cos(radians( ber.lat )) *
  haversin(radians( sm.lon - ber.lon )))) AS dist

The estimated distance between 'Berlin' and 'San Mateo' is returned.

Result
dist
`9129.969740051658`
Rows: 1

pi()

Details
Syntax	`pi()`
Description	Returns the mathematical constant pi.
Returns	`FLOAT`

Example 10. pi()

Query

RETURN pi()

The constant pi is returned.

Result
pi()
`3.141592653589793`
Rows: 1

radians()

Details
Syntax	`radians(input)`
Description	Converts degrees to radians.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in degrees.
Returns	`FLOAT`

Considerations
`radians(null)` returns `null`.

Example 11. radians()

Query

RETURN radians(180)

The number of radians in 180 degrees is returned (pi).

Result
radians(180)
`3.141592653589793`
Rows: 1

sin()

Details
Syntax	`sin(input)`
Description	Returns the sine of a `FLOAT`.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`sin(null)` returns `null`.

Example 12. sin()

Query

RETURN sin(0.5)

The sine of 0.5 is returned.

Result
sin(0.5)
`0.479425538604203`
Rows: 1

tan()

Details
Syntax	`tan(input)`
Description	Returns the tangent of a `FLOAT`.
Arguments	Name	Type	Description
	`input`	`FLOAT`	An angle in radians.
Returns	`FLOAT`

Considerations
`tan(null)` returns `null`.

Example 13. tan()

Query

RETURN tan(0.5)

The tangent of 0.5 is returned.

Result
tan(0.5)
`0.5463024898437905`
Rows: 1

Mathematical functions - trigonometric

acos()

asin()

atan()

atan2()

cos()

cot()

degrees()

haversin()

Spherical distance using the haversin() function

pi()

radians()

sin()

tan()

Spherical distance using the `haversin()` function