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| ACS | ASN | ATN | COS | SIN | TAN | PI |
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Name
ATN |
Syntax ATN(expression) |
Range
expression, Type real |
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Description
Returns the angle in the right angled triangle, which opposite to the adjacent are in proportion expression:1. This funcion is inverse to the tangent function TAN. |
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Example
s = y/x ! = gradient angle = ATN(s) |
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Tips and Tricks
The arc tangent offers not for all quadrants the correct angle related to the X-axis directly. One as to differ by the gradient (x/y) in the following cases: IF x=0 AND y=0 THEN angle=0 ELSE IF x THEN angle=ATN(y/x) ELSE angle=90+180*(y<0) IF angle<0 AND x<0 and y>0 THEN angle=180+angle IF angle>0 AND x<0 and y<0 THEN angle=180+angle IF angle<0 AND x>0 and y<0 THEN angle=angle+360 IF angle>=360 THEN angle=angle-360 ENDIF The same functionality in a compact code: IF x THEN angle=360*FRA((360+ATN(y/x)+(x<0)*180)/360) ELSE angle=90+180*(y<0) ENDIF |
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Links
Wikipedia: Einheitskreis Winkelfunktionen Arcus-Tangens Arcus-Cotangens Wolfram Research-Mathworld: Trigonometric functions |
References
GDL-Handbuch 4.5 (DE) p. 95 GDL-Handbuch 5.0 (DE) p. 126 GDL-Handbuch 6.0 (DE) p. 175 GDL-Handbuch 6.5 (DE) p. 177 GDL-Handbuch 7.0 (DE) p. 177 GDL-Handbuch 8.0 (DE) p. 120 GDL-Handbuch 8.1 (DE) p. 121 GDL-Handbuch 9.0 (DE) p. 200 GDL-Handbuch 10.0 (DE) p. 202 GDL-Handbuch 11.0 (DE) p. 208 GDL Reference Guide 9.0 (INT) p. 194 GDL Reference Guide 10.0 (INT) p. 200 GDL Reference Guide 11.0 (INT) p. 200 |
Abb. 1: Gradient at the unit circle
Abb. 2: The gradient rectangle.