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| Keyword | Abbreviation | Token (hex) | Version(s) | Classification |
| ATN | A{Shift+T} | C1 | 1.0+ | Function |
ATN ( slope )
| Parameters | Type | Legal Value(s) | Note(s) |
| slope | Numeric | | |
| Returns | Type | Value(s) | Note(s) |
| angle | Floating-point | -1.57079633 to +1.57079633 | the angle is in radians |
Calculate an angle which has the given slope.
The ATN function calculates an angle (measured in radians) with the given slope.
The slope can be described in a few (equivalant) ways: as the ratio of "rise" over "run",
or dy / dx, or the "trignometric tangent" (not to be confused with a geometric tangent).
If the slope is omitted or not a valid expression, SYNTAX ERROR is generated.
If slope is not numeric, a TYPE MISMATCH ERROR occurs.
The returned angle is in radians; it may converted to degrees by multiplying it by 180 / pi
(i.e., multiply the result by about 57.2958). The returned angle, measured in degrees,
will range from -90 to +90 (the radian range is shown in the table above).
This is only a span of half a circle (180 degees). To determine an angle anywhere
in the span of a full sircle (range of 360 degrees), additional information is required:
you need to know the sign of dx. If dx ("run") is positive,
then you can use the angle as-is.
Otherwise, add pi radians (180 degrees) to the returned angle.
Besides use in triginometry (directly) it may also be useful in other fields of engineering and science,
in particular for calculating the "phase angle" of a complex number
(very similar to the conversion from rectangular to polar coordinates).
ATN (arc tangent) is the priciple inverse of the TAN function.
Examples:
PRINT ATN(0)
0
READY.
PRINT ATN(1)
.785398163
READY.
PRINT ATN(1000)
1.56979633
READY. |
Although CBM BASIC offers SIN and COS functions, it doesn't offer ArcSin nor ArcCos functions.
These are often as important as ATN in software dealing with angles.
ArcSin and ArcCos functions can be calculated as shown in the following examples:
X=0.5:PRINT ATN(X/SQR(1-X*X)) :REM ArcSin(x) -- fails when |x|=1
.523598776
READY.
X=0.866:PRINT ATN(SQR(1-X*X)/X) :REM ArcCos(x) -- fails when x=0
.523649581
READY. |
LOG, SQR
TAN
π(pi), COS, SIN
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