ATAN() and ATAN2() Function in MySQL

1. ATAN() Function :
ATAN() function in MySQL is used to return the arc tangent of any number x. The arctangent of x is defined as the inverse tangent function of x when x is real (x∈ℝ).

When the tangent of y is equal to x :

tan y = x

Then the arctangent of x is equal to the inverse tangent function of x, which is equal to y :

arctan x= tan-1 x = y

Syntax :

ATAN(X)

Parameter : This method accepts one parameter as mentioned above and described below :

• X : A number whose arc tangent we want to calculate.

Returns : It returns the arc tangent of given number x.

Example-1 : Arc tangent of 1 using ATAN() function.

SELECT ATAN(1) AS Atan_Val ;

Output :

Atan_Val
0.7853981633974483

Example-2 : Arc tangent of  0 using ATAN() function.

SELECT ATAN(0) AS Atan_Val ;

Output :

Atan_Val
0

Example-3 : Arc tangent of  a +ve number in the range(0, -1)  using ATAN() function.

SELECT ATAN(0.35) AS Atan_Val ;

Output :

Atan_Val
0.33667481938672716

Example-4 : Arc tangent of  a -ve numbe using ATAN() function.

SELECT ATAN(-2.75) AS Atan_Val ;

Output :

Atan_Val
-1.2220253232109897

Example-5 : Arc tangent value of a numeric column in a table.

Table – Number :

X
-10
-1
-0.50
0
0.50
1
14

SELECT X, ATAN(X) AS ArcTan_X  FROM Number ;

Output :

X	ArcTan_X
-10	-1.4711276743037347
-1	-0.7853981633974483
-0.50	-0.4636476090008061
0	0
0.50	0.4636476090008061
1	0.7853981633974483
14	1.4994888620096063

2. ATAN2() Function :
ATAN2() function in MySQL is used for return the arc tangent between specified two number, i.e., x and y. It returns the angle between the positive x-axis and the line from the origin to the point (y, x).

Syntax :

ATAN2 (Y, X)

Parameter : This method accepts one parameter as mentioned above and described below :

• Y, X : Two number whose arc tangent we want to calculate.

Returns : It returns the angle between the positive x-axis and the line from the origin to the point (y, x).

Example-1 : Arc tangent of two negative number using ATAN2() function.

SELECT ATAN2(-5.44, -10.5 ) AS Atan2_Val ;

Output :

Atan2_Val
-2.6635738706445093

Example-2 : Arc tangent of two +ve number using ATAN2() function.

SELECT ATAN2( 20.35, 5.60 ) AS Atan2_Val ;

Output :

Atan2_Val
1.3022588047897063

Example-3 : Arc tangent value of two numeric column in a table.

Table – Number :

X	Y
3.5	2.5
-7.8	5
6.7	-1.2
-55.00	-12.00

SELECT X, Y, ATAN2(X, Y) AS ArcTan2_XY  FROM Number ;

Output :

X	Y	ArcTan2_XY
3.5	2.5	0.9505468408120752
-7.8	5	-1.0007558630951863
6.7	-1.2	-1.748021711744616
-55.00	-12.00	-1.7856117271965553