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Template:Atan2/doc
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The {{atan2}} circular function template returns the four quadrant arc tangent (a circular angle in radians as default, or a circular angle in radians) from and , which are real numbers not both zero.
Contents
Usage
- {{atan2|y=a real number|x=a real number|cut=an integer}}
or
- {{atan2|a real number|a real number|an integer}}
Valid input
- Two real numbers: and , not both zero. Third argument (optional) as integer, where an odd integer (default 1) implies a circular angle in radians and an even integer implies a circular angle in radians.
Examples
Examples with valid input
Code Result {{atan2|y=0|x=1|cut=1}} 0 {{atan2|y={{sin|pi/6}}|x={{cos|pi/6}}}} 0.5235987755983 {{atan2|y={{sin|pi/4}}|x={{cos|pi/4}}}} 0.78539816339745 {{atan2|y={{sin|pi/3}}|x={{cos|pi/3}}}} 1.0471975511966 {{atan2|y=1|x=0|cut=3}} 1.5707963267949 {{atan2|y={{sin|2*pi/3}}|x={{cos|2*pi/3}}}} 2.0943951023932 {{atan2|y={{sin|3*pi/4}}|x={{cos|3*pi/4}}}} 2.3561944901923 {{atan2|y={{sin|5*pi/6}}|x={{cos|5*pi/6}}}} 2.6179938779915 {{atan2|y=0|x=-1|cut=5}} 3.1415926535898 {{atan2|y={{sin|7*pi/6}}|x={{cos|7*pi/6}}}} -2.6179938779915 {{atan2|y={{sin|5*pi/4}}|x={{cos|5*pi/4}}}} -2.3561944901923 {{atan2|y={{sin|4*pi/3}}|x={{cos|4*pi/3}}}} -2.0943951023932 {{atan2|y=-1|x=0|cut=-1}} -1.5707963267949 {{atan2|y={{sin|5*pi/3}}|x={{cos|5*pi/3}}}} -1.0471975511966 {{atan2|y={{sin|7*pi/4}}|x={{cos|7*pi/4}}}} -0.78539816339745 {{atan2|y={{sin|11*pi/6}}|x={{cos|11*pi/6}}}} -0.5235987755983 {{atan2|y={{sin|2*pi}}|x={{cos|2*pi}}}} -2.4492935982947E-16
Code Result {{atan2|y=0|x=1|cut=0}} 0 {{atan2|y={{sin|pi/6}}|x={{cos|pi/6}}|cut=2}} 0.5235987755983 {{atan2|y={{sin|pi/4}}|x={{cos|pi/4}}|cut=2}} 0.78539816339745 {{atan2|y={{sin|pi/3}}|x={{cos|pi/3}}|cut=2}} 1.0471975511966 {{atan2|y=1|x=0|cut=2}} 1.5707963267949 {{atan2|y={{sin|2*pi/3}}|x={{cos|2*pi/3}}|cut=2}} 2.0943951023932 {{atan2|y={{sin|3*pi/4}}|x={{cos|3*pi/4}}|cut=2}} 2.3561944901923 {{atan2|y={{sin|5*pi/6}}|x={{cos|5*pi/6}}|cut=2}} 2.6179938779915 {{atan2|y=0|x=-1|cut=4}} 3.1415926535898 {{atan2|y={{sin|7*pi/6}}|x={{cos|7*pi/6}}|cut=2}} 3.6651914291881 {{atan2|y={{sin|5*pi/4}}|x={{cos|5*pi/4}}|cut=2}} 3.9269908169872 {{atan2|y={{sin|4*pi/3}}|x={{cos|4*pi/3}}|cut=2}} 4.1887902047864 {{atan2|y=-1|x=0|cut=-2}} 4.7123889803847 {{atan2|{{sin|5*pi/3}}|{{cos|5*pi/3}}|2}} 5.235987755983 {{atan2|{{sin|7*pi/4}}|{{cos|7*pi/4}}|2}} 5.4977871437821 {{atan2|{{sin|11*pi/6}}|{{cos|11*pi/6}}|2}} 5.7595865315813 {{atan2|y={{sin|2*pi}}|x={{cos|2*pi}}|cut=2}} 6.2831853071796
Examples with invalid input (returns an error message)
Code Result Comment {{atan2}} Atan2 error: Both arguments must be real numbers (not both zero) {{atan2|i}} Atan2 error: Both arguments must be real numbers (not both zero) {{atan2|2}} Atan2 error: Both arguments must be real numbers (not both zero) {{atan2|2|i}} Atan2 error: Both arguments must be real numbers (not both zero) {{atan2|i|2}} Atan2 error: Both arguments must be real numbers (not both zero) {{atan2|0|0}} Atan2 error: Result is undefined when both arguments are zero {{atan2|-1|0|2 pi}} Expression error: Unexpected < operator. {{atan2|-1|0|6.28}} 4.7123889803847 (parity of cut value rounded towards zero, please use integers for clarity) {{atan2|-1|0|6.7}} 4.7123889803847 (parity of cut value rounded towards zero, please use integers for clarity) {{atan2|-1|0|-6.28}} 4.7123889803847 (parity of cut value rounded towards zero, please use integers for clarity) {{atan2|-1|0|-6.7}} 4.7123889803847 (parity of cut value rounded towards zero, please use integers for clarity)
Code
<!-- Returns angle in (-pi, +pi] (default) or [0, 2*pi) -->{{ifnum| {{{y|{{{1|NAN}}}}}}{{{x|{{{2|NAN}}}}}}<!-- {{{cut|{{{3|1}}}}}} odd (for 1*pi, default) or even (for 2*pi) --> | {{#switch: {{#expr: 3*{{sgn| {{{y|{{{1}}}}}} }} + {{sgn| {{{x|{{{2}}}}}} }} }} | -4 = {{#expr: pi * {{#ifexpr: ({{{cut|{{{3|1}}}}}}) mod 2 = 0 | 1 | -1 }} + atan ( ({{{y|{{{1}}}}}}) / ({{{x|{{{2}}}}}}) ) }} <!-- y < 0 and x < 0 (third quadrant) --> | -3 = {{#expr: (pi / 2) * {{#ifexpr: ({{{cut|{{{3|1}}}}}}) mod 2 = 0 | 3 | -1 }} }} <!-- y < 0 and x = 0 --> | -2 = {{#expr: 2*pi * {{#ifexpr: ({{{cut|{{{3|1}}}}}}) mod 2 = 0 | 1 | 0 }} + atan ( ({{{y|{{{1}}}}}}) / ({{{x|{{{2}}}}}}) ) }} <!-- y < 0 and x > 0 (fourth quadrant) --> | -1 = {{#expr: pi }} <!-- y = 0 and x < 0 --> | 0 = {{error| Atan2 error: Result is undefined when both arguments are zero }} <!-- y = 0 and x = 0 --> | +1 = 0 <!-- y = 0 and x > 0 --> | +2 = {{#expr: pi + atan ( ({{{y|{{{1}}}}}}) / ({{{x|{{{2}}}}}}) ) }} <!-- y > 0 and x < 0 (second quadrant) --> | +3 = {{#expr: pi / 2 }} <!-- y > 0 and x = 0 --> | +4 = {{#expr: atan ( ({{{y|{{{1}}}}}}) / ({{{x|{{{2}}}}}}) ) }} <!-- y > 0 and x > 0 (first quadrant) --> }} | {{error| Atan2 error: Both arguments must be real numbers (not both zero) }} }}
See also