Trigonometric Functions
(COS, SIN, TAN, ACOS, ASIN, ATAN, ATAN2)
Purpose
Performs the trigonometric or inverse trigonometric function of an argument.
Syntax
where:
Syntax element … |
Specifies … |
arg |
any valid numeric expression that expresses an angle in radians. |
x |
the x-coordinate of a point to use in the arctangent calculation. |
y |
the y-coordinate of a point to use in the arctangent calculation. |
ANSI Compliance
This is a Teradata extension to the ANSI SQL:2011 standard.
Definitions
Function |
Definition |
Arccosine |
The arccosine is the angle whose cosine is the argument. |
Arcsine |
The arcsine is the angle whose sine is the argument. |
Arctangent |
The arctangent is the angle whose tangent is the argument. |
Cosine |
The cosine of an angle is the ratio of two sides of a right triangle. The ratio is the length of the side adjacent to the angle divided by the length of the hypotenuse. |
Sine |
The sine of an angle is the ratio of two sides of a right triangle. The ratio is the length of the side opposite to the angle divided by the length of the hypotenuse. |
Tangent |
The tangent of an angle is the ratio of two sides of a right triangle. The ratio is the length of the side opposite to the angle divided by the length of the side adjacent to the angle. |
Result Type and Attributes
Here are the default data type, format, and title for the result of the trigonometric and inverse trigonometric functions.
Data Type |
Format |
Title |
FLOAT |
Default format for FLOAT |
Cos(arg) |
For information on default data type formats, see SQL Data Types and Literals.
Result Value
Function |
Result Value |
COS(arg) |
The cosine of arg in radians in the range -1 to 1, inclusive. |
SIN(arg) |
The sine of arg in radians in the range -1 to 1, inclusive. |
TAN(arg) |
The tangent of arg in radians. |
ACOS(arg) |
An angle in the range 0 to π radians, inclusive. |
ASIN(arg) |
An angle in the range -π/2 to π/2 radians, inclusive. |
ATAN(arg) |
An angle in the range -π/2 to π/2 radians, inclusive. |
ATAN2(x,y) |
An angle between -π and π radians, excluding -π. A positive result represents a counterclockwise angle from the x-axis. A negative result represents a clockwise angle. ATAN2(x,y) equals ATAN(y/x), except that x can be 0 in ATAN2(x,y) and x cannot be 0 in ATAN(y/x) since this results in a divide by zero error. If both x and y are 0, an error is returned. |
Argument Types and Rules
Arguments that are not FLOAT are converted to FLOAT based on implicit type conversion rules. If an argument cannot be converted, an error is reported. For more information on implicit type conversion, see “Implicit Type Conversions” on page 583.
If an argument is a UDT, the following rules apply:
To define an implicit cast for a UDT, use the CREATE CAST statement and specify the AS ASSIGNMENT clause. For more information on CREATE CAST, see SQL Data Definition Language.
Trigonometric and inverse trigonometric functions cannot take the following types of arguments:
Examples
The following are representative function expressions and results.
Expression |
Result |
COS(5-4) |
5.40302305868140E -001 |
SIN(LOG(0.5)) |
-2.96504042171437E -001 |
SIN(RADIANS(180.0)) |
1.22464679914735E-016 |
TAN(ABS(-3)) |
-1.42546543074278E -001 |
ACOS(-0.5) |
2.09439510239320E 000 |
ASIN(1) |
1.57079632679490E 000 |
ATAN(1+2) |
1.24904577239825E 000 |
ATAN2(1,1) |
7.85398163397448E -001 |