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# Trigonometric Functions

The following functions are useful for working with angles and performing various trigonometric calculations.

degrees

Converts angle units from radians into degrees.

Syntax: | degrees(Angle)
Arguments: | Angle is the angle in radians that you want to convert.
Examples: | degrees(PI) returns 180. degrees(PI/2) returns 90.

radians

Converts angle units from degrees into radians.

Syntax: | radians(Angle)
Arguments: | Angle is the angle in degrees that you want to convert.
Example: | radians(225) returns 3.927 (5*PI/4).

cos

Returns the cosine of a given angle.

Syntax: | cos(Angle)
Arguments: | Angle is the angle in radians of which you want the cosine.
Examples: | cos(0) returns 1. cos(PI / 3) returns 0.5. cos(frame / 10) * 100 yields the following curve:

sin

Returns the sine of a given angle.

Syntax: | sin(Angle)
Arguments: | Angle is the angle in radians of which you want the sine.
Examples: | sin(0) returns 0. sin(PI / 6) returns 0.5. sin(frame / 10) * 100 yields the following curve:

tan

Returns the tangent of a given angle.

Syntax: | tan(Angle)
Arguments: | Angle is the angle in radians of which you want the tangent.
Examples: | tan(0) returns 0. tan(PI / 4) returns 1. tan(PI / 3) returns 1.7321. tan(frame / 10) * 50 yields the following curve:

acos

Returns the arccosine—the inverse function of the cosine—of a given number. The returned angle is given in radians within the range 0 to PI.

Syntax: | acos(Number)
Arguments: | Number is the cosine of the angle you want and must be between-1 and 1.
Examples: | acos(0.5) returns 1.0472 (PI/3 radians). degrees(acos(0.5)) returns 60.

asin

Returns the arcsine—the inverse function of the sine—of a given number. The returned angle is given in radians within the range -PI/2 to PI/2.

Syntax: | asin(Number)
Arguments: | Number is the sine of the angle you want and must be between-1 and 1.
Examples: | asin(0.5) returns 0.5236 (PI/6 radians). degrees(asin(0.5)) returns 30.

atan

Returns the arctangent—the inverse function of the tangent— of a given number. The returned angle is given in radians within the range -PI/2 to PI/2.

Syntax: | atan(Number)
Arguments: | Number is the tangent of the angle you want.
Examples: | atan(1) returns 0.7854 (PI/4 radians). degrees(atan(1)) returns 45.

atan2

Returns the arctangent of y/x, using the signs of both arguments to determine the quadrant of the return value. The arctangent is the angle from the origin to the vector (x,y). The returned angle is given in radians within the range -PI to PI.

Syntax: | atan2(x, y)
Arguments: | x and y are the components of the vector to be used in the function.
Examples: | atan2(1, 1) returns 0.7854 (PI/4 radians). atan2(-1, -1) returns -2.3562 (-3*PI/4 radians). atan2(1, 0) returns 1.5708 (PI/2 radians). degrees(atan2(1,1)) returns 45.