Trigonometry SIN COS

Angles are in Radians, not Degrees. All computations are done in IEEE 754 64-bit floating point. All floating point computations are subject to small errors, known as machine ε (epsilon) errors, so avoid trying to compare them for equality. There is no way to avoid these errors when using floating point; they are built in to the technology.

If you use DECIMAL values in trigonometric computations, they are implicitly converted to floating point, and then back to decimal.

Sine

Returns the sine of a number X expressed in radians

SELECT SIN(PI()); -> 1.2246063538224e-16

Cosine

Returns the cosine of X when X is given in radians

SELECT COS(PI()); -> -1

Tangent

Returns the tangent of a number X expressed in radians. Notice the result is very close to zero, but not exactly zero. This is an example of machine ε.

SELECT TAN(PI());   -> -1.2246063538224e-16

Arc Cosine (inverse cosine)

Returns the arc cosine of X if X is in the range -1 to 1

SELECT ACOS(1);    -> 0
SELECT ACOS(1.01); -> NULL

Arc Sine (inverse sine)

Returns the arc sine of X if X is in the range -1 to 1

SELECT ASIN(0.2); -> 0.20135792079033

Arc Tangent (inverse tangent)

ATAN(x) returns the arc tangent of a single number.

SELECT ATAN(2); -> 1.1071487177941

ATAN2(X, Y) returns the arc tangent of the two variables X and Y. It is similar to calculating the arc tangent of Y / X. But it is numerically more robust: t functions correctly when X is near zero, and the signs of both arguments are used to determine the quadrant of the result.

Best practice suggests writing formulas to use ATAN2() rather than ATAN() wherever possible.

ATAN2(1,1);    -> 0.7853981633974483 (45 degrees)
ATAN2(1,-1);   -> 2.356194490192345  (135 degrees)
ATAN2(0, -1);  -> PI  (180 degrees)  don't try ATAN(-1 / 0)... it won't work

Cotangent

Returns the cotangent of X

SELECT COT(12); -> -1.5726734063977

Conversion

SELECT RADIANS(90) -> 1.5707963267948966
SELECT SIN(RADIANS(90)) -> 1
SELECT DEGREES(1), DEGREES(PI()) -> 57.29577951308232, 180