docs/functions/trigonometric_functions.md

# Trigonometric Functions


## degrees

degrees() converts radians to degrees.

Syntax:`degrees(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* degrees(null) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN degrees(3.14159)
$$) as (deg agtype);
```


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

Results:


<table>
  <tr>
   <td>deg
   </td>
  </tr>
  <tr>
   <td>179.99984796050427
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## radians

radians() converts radians to degrees.

Syntax:`radians(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in degrees.
   </td>
  </tr>
</table>


Considerations:



* radians(null) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN radians(180)
$$) as (rad agtype);
```


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

Results:


<table>
  <tr>
   <td>rad
   </td>
  </tr>
  <tr>
   <td>3.14159265358979
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## pi

pi() returns the mathematical constant pi.

Syntax: `pi()`

Returns:


```
An agtype float.
```


Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN pi()
$$) as (p agtype);
```


The constant pi is returned.

Result:


<table>
  <tr>
   <td>p
   </td>
  </tr>
  <tr>
   <td>3.141592653589793
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## sin

sin() returns the sine of a number.

Syntax:`sin(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* sin(null) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN sin(0.5)
$$) as (s agtype);
```


The sine of 0.5 is returned.

Results:


<table>
  <tr>
   <td>s
   </td>
  </tr>
  <tr>
   <td>0.479425538604203
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## cos

cos() returns the cosine of a number.

Syntax: `cos(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* cos(null) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN cosin(0.5)
$$) as (c agtype);
```


The cosine of 0.5 is returned.

Results:


<table>
  <tr>
   <td>c
   </td>
  </tr>
  <tr>
   <td>0.8775825618903728
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## tan

tan() returns the tangent of a number.

Syntax: `tan(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* tan(null) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN tan(0.5)
$$) as (t agtype);
```


The tangent of 0.5 is returned.

Results:


<table>
  <tr>
   <td>t
   </td>
  </tr>
  <tr>
   <td>0.5463024898437905
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## asin

asin() returns the arcsine of a number.

Syntax:`asin(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* asin(null) returns null.
* If (expression &lt; -1) or (expression > 1), then (asin(expression)) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN asin(0.5)
$$) as (s agtype);
```


The arcsine of 0.5 is returned.

Results:


<table>
  <tr>
   <td>s
   </td>
  </tr>
  <tr>
   <td>0.523598775598299
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## acos

acos() returns the arccosine of a number.

Syntax:`acos(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* acos(null) returns null.
* If (expression &lt; -1) or (expression > 1), then (acos(expression)) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN acos(0.5)
$$) as (arc_c agtype);
```


The arccosine of 0.5 is returned.

Results:


<table>
  <tr>
   <td>arc_c
   </td>
  </tr>
  <tr>
   <td>1.0471975511965979
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## atan

atan() returns the arctangent of a number.

Syntax:`atan(expression)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression
   </td>
   <td>An agtype number expression that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* atan(null) returns null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN atan(0.5)
$$) as (arc_t agtype);
```


The arccosine of 0.5 is returned.

Results:


<table>
  <tr>
   <td>arc_t
   </td>
  </tr>
  <tr>
   <td>0.463647609000806
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>



## atan2

atan2() returns the arctangent2 of a set of coordinates in radians.

Syntax: `atan2(expression1, expression2)`

Returns:


```
A Float.
```


Arguments:


<table>
  <tr>
   <td>Name
   </td>
   <td>Description
   </td>
  </tr>
  <tr>
   <td>expression1
   </td>
   <td>An agtype number expression for y that represents the angle in radians.
   </td>
  </tr>
  <tr>
   <td>expression2
   </td>
   <td>An agtype number expression for x that represents the angle in radians.
   </td>
  </tr>
</table>


Considerations:



* atan2(null, null), atan2(null, expression2) and atan(expression1, null) all return null.

Query:


```
SELECT *
FROM cypher('graph_name', $$
    RETURN atan2(0.5, 0.6)
$$) as (arc_t2 agtype);
```


The arctangent2 of 0.5 and 0.6 is returned.

Results:


<table>
  <tr>
   <td>arc_t2
   </td>
  </tr>
  <tr>
   <td>0.694738276196703
   </td>
  </tr>
  <tr>
   <td>1 row(s) returned
   </td>
  </tr>
</table>