ATN function

Purpose | Return the arctangent of an argument.
Syntax | y = ATN(numeric_expression)

Remarks

ATN returns the arctangent (Inverse Tangent) of numeric_expression; that is, the angle whose tangent is numeric_expression.

The result, as with all operations involving angles in PowerBASIC, is in radians rather than degrees. Although it is common to specify angles in degrees, the radian is a more convenient measurement for mathematical operations. One radian is defined as the angle at the center of a circle that subtends an arc equal in length to one radius. Since for all circles, using the constant π:

Circumference / radius = 2 * π

the length of the circumference of a circle is equal to 2 * π * radius, and the angle of a full circle (360 degrees) is equal to 2 * π radians.

To convert radians to degrees, just multiply the radian value by 180/π, or 57.29577951308232##. For example, the arctangent of 0.23456 can be converted this way:

t = ATN(.23456!) 't = 0.230395 (radians)

t = 57.29577951308232## * ATN(.23456!) 't= 13.200 (degrees)

To convert degrees to radians, multiply by 0.0174532925199433##. For example:

14 degrees = (0.0174532925199433## * 14) = 0.2443460952792062 radians

Rather than memorizing the radians/degrees conversion factors, calculate them for yourself by remembering this relationship: 2 π radians equals a full circle (360 degrees), so 1 π radian is 180 / π degrees. Conversely, 1 degree equals π / 180 radians.

π is a transcendental constant, meaning that it has an infinite number of decimal places. To 15-place accuracy, adequate for most applications, π = 3.141592653589793##. This value can be closely approximated with the expression:

pi## = 4 * ATN(1)

Degrees-to-radians and radians-to-degrees conversions are good applications for user-defined functions.

The ATN function always returns an Extended-precision result.

The Tangent (TAN) of a value can be easily calculated with the TAN function.

The Hyperbolic Tangent (TANH) can be calculated:

TanH = (EXP(2 * Value) - 1) / (EXP(2 * Value) + 1)

The Inverse Hyperbolic Tangent (ARCTANH) of a value can be calculated:

ArcTanH = LOG((1 + Value) / (1 - Value)) / 2

' Useful Macro functions

MACRO Pi = 3.141592653589793##

MACRO DegreesToRadians(dpDegrees) = (dpDegrees*0.0174532925199433##)

MACRO RadiansToDegrees(dpRadians) = (dpRadians*57.29577951308232##)

See also | COS, SIN, TAN