# Trigonometric functions Trigonometric function reference documentation. This page describes the available functions to assist with performing trigonometric calculations. :::tip Positive and negative infinity values are expressed as `'Infinity'` or `'-Infinity'` in QuestDB. ::: ## acos `acos(value)` returns the arccosine of a value. ### Arguments - `value` is a numeric value whose arccosine is to be returned. The returned angle is between 0.0 and pi inclusively. ### Return value Return value type is `double`. ### Description Special cases: if the argument is `NaN` or its absolute value is greater than 1, then the result is `Null`. ### Examples ```questdb-sql SELECT acos(0.0) acos; ``` | acos | | -------------- | | 1.570796326794 | ## asin `asin(value)` the arcsine of a value. ### Arguments - `value` is a numeric value whose arcsine is to be returned. ### Return value Return value type is `double`. The returned angle is between -pi/2 and pi/2 inclusively. ### Description Special case: if the argument is `NaN` or an infinity, then the result is `Null`. ### Examples ```questdb-sql SELECT asin(1.0) asin; ``` | asin | | -------------- | | 1.570796326794 | ## atan `atan(value)` returns the arctangent of a value. ### Arguments - `value` is a numeric value whose arctangent is to be returned. ### Return value Return value type is `double`. The returned angle is between -pi/2 and pi/2 inclusively. ### Description Special cases: - If the argument is `NaN`, then the result is `Null`. - If the argument is infinity, then the result is the closest value to pi/2 with the same sign as the input. ### Examples Special case where input is `'-Infinity'`: ```questdb-sql SELECT atan('-Infinity'); ``` Returns the closest value to pi/2 with the same sign as the input: | atan | | --------------- | | -1.570796326794 | ```questdb-sql SELECT atan(1.0) atan; ``` | atan | | -------------- | | 0.785398163397 | ## atan2 `atan2(valueY, valueX)` returns the angle _theta_ from the conversion of rectangular coordinates (x, y) to polar (r, theta). This function computes _theta_ (the phase) by computing an arctangent of y/x in the range of -pi to pi inclusively. ### Arguments - `valueY` numeric ordinate coordinate. - `valueX` numeric abscissa coordinate. :::note The arguments to this function pass the y-coordinate first and the x-coordinate second. ::: ### Return value Return value type is `double` between -pi and pi inclusively. ### Description: `atan2(valueY, valueX)` measures the counterclockwise angle _theta_, in radians, between the positive x-axis and the point (x, y): Special cases: | input `valueY` | input `valueX` | `atan2` return value | | --------------------- | -------------- | ---------------------------------- | | 0 | Positive value | 0 | | Positive finite value | 'Infinity' | 0 | | -0 | Positive value | 0 | | Negative finite value | 'Infinity' | 0 | | 0 | Negative value | Double value closest to pi | | Positive finite value | '-Infinity' | Double value closest to pi | | -0 | Negative value | Double value closest to -pi | | Negative finite value | '-Infinity' | Double value closest to -pi | | Positive value | 0 or -0 | Double value closest to pi/2 | | 'Infinity' | Finite value | Double value closest to pi/2 | | Negative value | 0 or -0 | Double value closest to -pi/2 | | '-Infinity' | Finite value | Double value closest to -pi/2 | | 'Infinity' | 'Infinity' | Double value closest to pi/4 | | 'Infinity' | '-Infinity' | Double value closest to 3/4 \* pi | | '-Infinity' | 'Infinity' | Double value closest to -pi/4 | | '-Infinity' | '-Infinity' | Double value closest to -3/4 \* pi | ### Examples ```questdb-sql SELECT atan2(1.0, 1.0) atan2; ``` | atan2 | | -------------- | | 0.785398163397 | ## cos `cos(angleRadians)` returns the trigonometric cosine of an angle. ### Arguments - `angleRadians` numeric value for the angle, in radians. ### Return value Return value type is `double`. ### Description Special case: if the argument is `NaN` or an infinity, then the result is `Null`. ### Examples ```questdb-sql SELECT pi()/2 angle, cos(pi()/2) cos; ``` | angle | cos | | -------------- | --------------------- | | 1.570796326794 | 6.123233995736766e-17 | ## cot `cot(angleRadians)` returns the trigonometric cotangent of an angle. ### Arguments - `angleRadians` numeric value for the angle, in radians. ### Return value Return value type is `double`. ### Description Special case: if the argument is `NaN`, 0, or an infinity, then the result is `Null`. ### Examples ```questdb-sql SELECT pi()/2 angle, cot(pi()/2) cot; ``` | angle | cot | | -------------- | --------------------- | | 1.570796326794 | 6.123233995736766e-17 | ## degrees `degrees(angleRadians)` converts an angle measured in radians to the equivalent angle measured in degrees. ### Arguments - `angleRadians` numeric value for the angle in radians. ### Return value Return value type is `double`. ### Examples ```questdb-sql SELECT degrees(pi()); ``` | degrees | | ------- | | 180 | ## pi `pi()` returns the constant pi as a double. ### Arguments None. ### Return value Return value type is `double`. ### Examples ```questdb-sql SELECT pi(); ``` | pi | | -------------- | | 3.141592653589 | ## radians `radians(angleDegrees)` converts an angle measured in degrees to the equivalent angle measured in radians. ### Arguments - `angleDegrees` numeric value for the angle in degrees. ### Return value Return value type is `double`. ### Examples ```questdb-sql SELECT radians(180); ``` | radians | | -------------- | | 3.141592653589 | ## sin `sin(angleRadians)` returns the trigonometric sine of an angle. ### Arguments - `angleRadians` is a numeric value indicating the angle in radians. ### Return value Return value type is `double`. ### Description Special case: if the argument is `NaN` or an infinity, then the result is `Null`. ### Examples ```questdb-sql SELECT pi()/2 angle, sin(pi()/2) sin; ``` | angle | sin | | -------------- | --- | | 1.570796326794 | 1 | ## tan `tan(angleRadians)` returns the trigonometric tangent of an angle. ### Arguments - `angleRadians` numeric value for the angle, in radians. ### Return value Return value type is `double`. ### Description Special case: if the argument is `NaN` or an infinity, then the result is `Null`. ### Examples ```questdb-sql SELECT pi()/2 angle, tan(pi()/2) tan; ``` | angle | tan | | -------------- | ----------------- | | 1.570796326794 | 16331239353195370 |