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Plotting a function graph/ sin(x)*atan(x)

Graphing y = sin(x)*atan(x)

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = sin(x)*atan(x)
f(x)=sin⁡(x)atan⁡(x)f{\left(x \right)} = \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} 
f = sin(x)*atan(x)
The graph of the function
02468-8-6-4-2-10105-5
The points of intersection with the X-axis coordinate
Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
sin⁡(x)atan⁡(x)=0\sin{\left(x \right)} \operatorname{atan}{\left(x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
x2=πx_{2} = \pi
Numerical solution
x1=62.8318530717959x_{1} = 62.8318530717959
x2=−50.2654824574367x_{2} = -50.2654824574367
x3=47.1238898038469x_{3} = 47.1238898038469
x4=84.8230016469244x_{4} = 84.8230016469244
x5=−53.4070751110265x_{5} = -53.4070751110265
x6=91.106186954104x_{6} = 91.106186954104
x7=−84.8230016469244x_{7} = -84.8230016469244
x8=25.1327412287183x_{8} = 25.1327412287183
x9=−3.14159265358979x_{9} = -3.14159265358979
x10=−6.28318530717959x_{10} = -6.28318530717959
x11=−40.8407044966673x_{11} = -40.8407044966673
x12=292.168116783851x_{12} = 292.168116783851
x13=−18.8495559215388x_{13} = -18.8495559215388
x14=78.5398163397448x_{14} = 78.5398163397448
x15=−75.398223686155x_{15} = -75.398223686155
x16=−9.42477796076938x_{16} = -9.42477796076938
x17=72.2566310325652x_{17} = 72.2566310325652
x18=−43.9822971502571x_{18} = -43.9822971502571
x19=31.4159265358979x_{19} = 31.4159265358979
x20=9.42477796076938x_{20} = 9.42477796076938
x21=40.8407044966673x_{21} = 40.8407044966673
x22=−69.1150383789755x_{22} = -69.1150383789755
x23=12.5663706143592x_{23} = 12.5663706143592
x24=87.9645943005142x_{24} = 87.9645943005142
x25=59.6902604182061x_{25} = 59.6902604182061
x26=−37.6991118430775x_{26} = -37.6991118430775
x27=−100.530964914873x_{27} = -100.530964914873
x28=−91.106186954104x_{28} = -91.106186954104
x29=97.3893722612836x_{29} = 97.3893722612836
x30=0x_{30} = 0
x31=−12.5663706143592x_{31} = -12.5663706143592
x32=−78.5398163397448x_{32} = -78.5398163397448
x33=18.8495559215388x_{33} = 18.8495559215388
x34=34.5575191894877x_{34} = 34.5575191894877
x35=−94.2477796076938x_{35} = -94.2477796076938
x36=43.9822971502571x_{36} = 43.9822971502571
x37=−31.4159265358979x_{37} = -31.4159265358979
x38=−81.6814089933346x_{38} = -81.6814089933346
x39=−65.9734457253857x_{39} = -65.9734457253857
x40=75.398223686155x_{40} = 75.398223686155
x41=56.5486677646163x_{41} = 56.5486677646163
x42=−122.522113490002x_{42} = -122.522113490002
x43=3.14159265358979x_{43} = 3.14159265358979
x44=15.707963267949x_{44} = 15.707963267949
x45=−56.5486677646163x_{45} = -56.5486677646163
x46=−21.9911485751286x_{46} = -21.9911485751286
x47=50.2654824574367x_{47} = 50.2654824574367
x48=−15.707963267949x_{48} = -15.707963267949
x49=28.2743338823081x_{49} = 28.2743338823081
x50=163.362817986669x_{50} = 163.362817986669
x51=94.2477796076938x_{51} = 94.2477796076938
x52=−59.6902604182061x_{52} = -59.6902604182061
x53=−62.8318530717959x_{53} = -62.8318530717959
x54=69.1150383789755x_{54} = 69.1150383789755
x55=−34.5575191894877x_{55} = -34.5575191894877
x56=1030.44239037745x_{56} = 1030.44239037745
x57=21.9911485751286x_{57} = 21.9911485751286
x58=−97.3893722612836x_{58} = -97.3893722612836
x59=65.9734457253857x_{59} = 65.9734457253857
x60=37.6991118430775x_{60} = 37.6991118430775
x61=−72.2566310325652x_{61} = -72.2566310325652
x62=−87.9645943005142x_{62} = -87.9645943005142
x63=−25.1327412287183x_{63} = -25.1327412287183
x64=−28.2743338823081x_{64} = -28.2743338823081
x65=81.6814089933346x_{65} = 81.6814089933346
x66=6.28318530717959x_{66} = 6.28318530717959
x67=100.530964914873x_{67} = 100.530964914873
x68=53.4070751110265x_{68} = 53.4070751110265
x69=−47.1238898038469x_{69} = -47.1238898038469
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to sin(x)*atan(x).
sin⁡(0)atan⁡(0)\sin{\left(0 \right)} \operatorname{atan}{\left(0 \right)}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
Extrema of the function
In order to find the extrema, we need to solve the equation
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(the derivative equals zero),
and the roots of this equation are the extrema of this function:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
the first derivative
cos⁡(x)atan⁡(x)+sin⁡(x)x2+1=0\cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{\sin{\left(x \right)}}{x^{2} + 1} = 0
Solve this equation
The roots of this equation
x1=−48.694958052076x_{1} = -48.694958052076
x2=−11.0011109024118x_{2} = -11.0011109024118
x3=−7.8649958747173x_{3} = -7.8649958747173
x4=26.7044507808002x_{4} = 26.7044507808002
x5=29.8458596412272x_{5} = 29.8458596412272
x6=23.5631212086715x_{6} = 23.5631212086715
x7=−89.5354705986824x_{7} = -89.5354705986824
x8=0x_{8} = 0
x9=−26.7044507808002x_{9} = -26.7044507808002
x10=−92.6770579048997x_{10} = -92.6770579048997
x11=−42.4118599365484x_{11} = -42.4118599365484
x12=95.8186457300403x_{12} = 95.8186457300403
x13=51.8365185642119x_{13} = 51.8365185642119
x14=58.1196545885159x_{14} = 58.1196545885159
x15=73.827545153735x_{15} = 73.827545153735
x16=7.8649958747173x_{16} = 7.8649958747173
x17=−51.8365185642119x_{17} = -51.8365185642119
x18=11.0011109024118x_{18} = 11.0011109024118
x19=−70.6859632509207x_{19} = -70.6859632509207
x20=−95.8186457300403x_{20} = -95.8186457300403
x21=42.4118599365484x_{21} = 42.4118599365484
x22=64.4028043800929x_{22} = 64.4028043800929
x23=−54.9780844551589x_{23} = -54.9780844551589
x24=89.5354705986824x_{24} = 89.5354705986824
x25=−1.79103397776014x_{25} = -1.79103397776014
x26=−23.5631212086715x_{26} = -23.5631212086715
x27=67.5443828898684x_{27} = 67.5443828898684
x28=−45.5534044627264x_{28} = -45.5534044627264
x29=−4.74359618362999x_{29} = -4.74359618362999
x30=39.2703275097022x_{30} = 39.2703275097022
x31=20.4219240188353x_{31} = 20.4219240188353
x32=48.694958052076x_{32} = 48.694958052076
x33=92.6770579048997x_{33} = 92.6770579048997
x34=61.2612281128569x_{34} = 61.2612281128569
x35=70.6859632509207x_{35} = 70.6859632509207
x36=83.2522978663322x_{36} = 83.2522978663322
x37=36.1288116046131x_{37} = 36.1288116046131
x38=−29.8458596412272x_{38} = -29.8458596412272
x39=−14.1404840184881x_{39} = -14.1404840184881
x40=80.1107126426188x_{40} = 80.1107126426188
x41=−61.2612281128569x_{41} = -61.2612281128569
x42=−80.1107126426188x_{42} = -80.1107126426188
x43=−17.2809654364073x_{43} = -17.2809654364073
x44=54.9780844551589x_{44} = 54.9780844551589
x45=−58.1196545885159x_{45} = -58.1196545885159
x46=98.9602340090719x_{46} = 98.9602340090719
x47=−86.3938838884988x_{47} = -86.3938838884988
x48=−64.4028043800929x_{48} = -64.4028043800929
x49=17.2809654364073x_{49} = 17.2809654364073
x50=32.987318864864x_{50} = 32.987318864864
x51=−76.9691283508747x_{51} = -76.9691283508747
x52=14.1404840184881x_{52} = 14.1404840184881
x53=−39.2703275097022x_{53} = -39.2703275097022
x54=−32.987318864864x_{54} = -32.987318864864
x55=−73.827545153735x_{55} = -73.827545153735
x56=−98.9602340090719x_{56} = -98.9602340090719
x57=−83.2522978663322x_{57} = -83.2522978663322
x58=1.79103397776014x_{58} = 1.79103397776014
x59=86.3938838884988x_{59} = 86.3938838884988
x60=−36.1288116046131x_{60} = -36.1288116046131
x61=−20.4219240188353x_{61} = -20.4219240188353
x62=−67.5443828898684x_{62} = -67.5443828898684
x63=45.5534044627264x_{63} = 45.5534044627264
x64=76.9691283508747x_{64} = 76.9691283508747
x65=4.74359618362999x_{65} = 4.74359618362999
The values of the extrema at the points:
(-48.694958052076046, -1.55026314860543)

(-11.001110902411808, -1.4801228582299)

(-7.864995874717303, 1.44424164730901)

(26.704450780800197, 1.53336623503182)

(29.84585964122719, -1.53730296241164)

(23.56312120867149, -1.52838152134177)

(-89.53547059868244, 1.55962802821361)

(0, 0)

(-26.704450780800197, 1.53336623503182)

(-92.6770579048997, -1.5600065842339)

(-42.41185993654844, -1.54722228447912)

(95.8186457300403, 1.56036031976415)

(51.83651856421186, 1.55150725579965)

(58.119654588515886, 1.55359211279627)

(73.82754515373497, -1.5572520643401)

(7.864995874717303, 1.44424164730901)

(-51.83651856421186, 1.55150725579965)

(11.001110902411808, -1.4801228582299)

(-70.68596325092066, 1.55665017729342)

(-95.8186457300403, 1.56036031976415)

(42.41185993654844, -1.54722228447912)

(64.4028043800929, 1.5552702816364)

(-54.97808445515894, -1.55260923119595)

(89.53547059868244, 1.55962802821361)

(-1.7910339777601358, 1.03593336473382)

(-23.56312120867149, -1.52838152134177)

(67.54438288986843, -1.55599231281641)

(-45.553404462726384, 1.54884752107669)

(-4.7435961836299905, -1.36236430357899)

(39.270327509702184, 1.54533717389503)

(20.42192401883534, 1.52186654514573)

(48.694958052076046, -1.55026314860543)

(92.6770579048997, -1.5600065842339)

(61.26122811285691, -1.5544742153389)

(70.68596325092066, 1.55665017729342)

(83.25229786633224, 1.55878521728754)

(36.128811604613105, -1.54312446153498)

(-29.84585964122719, -1.53730296241164)

(-14.140484018488104, 1.50018667629801)

(80.11071264261882, -1.55831424223611)

(-61.26122811285691, -1.5544742153389)

(-80.11071264261882, -1.55831424223611)

(-17.280965436407328, -1.51298997049872)

(54.97808445515894, -1.55260923119595)

(-58.119654588515886, 1.55359211279627)

(98.96023400907185, -1.56069159831347)

(-86.39388388849885, -1.55922194448498)

(-64.4028043800929, 1.5552702816364)

(17.280965436407328, -1.51298997049872)

(32.98731886486398, 1.54049065473337)

(-76.96912835087466, 1.55780482663327)

(14.140484018488104, 1.50018667629801)

(-39.270327509702184, 1.54533717389503)

(-32.98731886486398, 1.54049065473337)

(-73.82754515373497, -1.5572520643401)

(-98.96023400907185, -1.56069159831347)

(-83.25229786633224, 1.55878521728754)

(1.7910339777601358, 1.03593336473382)

(86.39388388849885, -1.55922194448498)

(-36.128811604613105, -1.54312446153498)

(-20.42192401883534, 1.52186654514573)

(-67.54438288986843, -1.55599231281641)

(45.553404462726384, 1.54884752107669)

(76.96912835087466, 1.55780482663327)

(4.7435961836299905, -1.36236430357899)


Intervals of increase and decrease of the function:
Let's find intervals where the function increases and decreases, as well as minima and maxima of the function, for this let's look how the function behaves itself in the extremas and at the slightest deviation from:
Minima of the function at points:
x1=−48.694958052076x_{1} = -48.694958052076
x2=−11.0011109024118x_{2} = -11.0011109024118
x3=29.8458596412272x_{3} = 29.8458596412272
x4=23.5631212086715x_{4} = 23.5631212086715
x5=0x_{5} = 0
x6=−92.6770579048997x_{6} = -92.6770579048997
x7=−42.4118599365484x_{7} = -42.4118599365484
x8=73.827545153735x_{8} = 73.827545153735
x9=11.0011109024118x_{9} = 11.0011109024118
x10=42.4118599365484x_{10} = 42.4118599365484
x11=−54.9780844551589x_{11} = -54.9780844551589
x12=−23.5631212086715x_{12} = -23.5631212086715
x13=67.5443828898684x_{13} = 67.5443828898684
x14=−4.74359618362999x_{14} = -4.74359618362999
x15=48.694958052076x_{15} = 48.694958052076
x16=92.6770579048997x_{16} = 92.6770579048997
x17=61.2612281128569x_{17} = 61.2612281128569
x18=36.1288116046131x_{18} = 36.1288116046131
x19=−29.8458596412272x_{19} = -29.8458596412272
x20=80.1107126426188x_{20} = 80.1107126426188
x21=−61.2612281128569x_{21} = -61.2612281128569
x22=−80.1107126426188x_{22} = -80.1107126426188
x23=−17.2809654364073x_{23} = -17.2809654364073
x24=54.9780844551589x_{24} = 54.9780844551589
x25=98.9602340090719x_{25} = 98.9602340090719
x26=−86.3938838884988x_{26} = -86.3938838884988
x27=17.2809654364073x_{27} = 17.2809654364073
x28=−73.827545153735x_{28} = -73.827545153735
x29=−98.9602340090719x_{29} = -98.9602340090719
x30=86.3938838884988x_{30} = 86.3938838884988
x31=−36.1288116046131x_{31} = -36.1288116046131
x32=−67.5443828898684x_{32} = -67.5443828898684
x33=4.74359618362999x_{33} = 4.74359618362999
Maxima of the function at points:
x33=−7.8649958747173x_{33} = -7.8649958747173
x33=26.7044507808002x_{33} = 26.7044507808002
x33=−89.5354705986824x_{33} = -89.5354705986824
x33=−26.7044507808002x_{33} = -26.7044507808002
x33=95.8186457300403x_{33} = 95.8186457300403
x33=51.8365185642119x_{33} = 51.8365185642119
x33=58.1196545885159x_{33} = 58.1196545885159
x33=7.8649958747173x_{33} = 7.8649958747173
x33=−51.8365185642119x_{33} = -51.8365185642119
x33=−70.6859632509207x_{33} = -70.6859632509207
x33=−95.8186457300403x_{33} = -95.8186457300403
x33=64.4028043800929x_{33} = 64.4028043800929
x33=89.5354705986824x_{33} = 89.5354705986824
x33=−1.79103397776014x_{33} = -1.79103397776014
x33=−45.5534044627264x_{33} = -45.5534044627264
x33=39.2703275097022x_{33} = 39.2703275097022
x33=20.4219240188353x_{33} = 20.4219240188353
x33=70.6859632509207x_{33} = 70.6859632509207
x33=83.2522978663322x_{33} = 83.2522978663322
x33=−14.1404840184881x_{33} = -14.1404840184881
x33=−58.1196545885159x_{33} = -58.1196545885159
x33=−64.4028043800929x_{33} = -64.4028043800929
x33=32.987318864864x_{33} = 32.987318864864
x33=−76.9691283508747x_{33} = -76.9691283508747
x33=14.1404840184881x_{33} = 14.1404840184881
x33=−39.2703275097022x_{33} = -39.2703275097022
x33=−32.987318864864x_{33} = -32.987318864864
x33=−83.2522978663322x_{33} = -83.2522978663322
x33=1.79103397776014x_{33} = 1.79103397776014
x33=−20.4219240188353x_{33} = -20.4219240188353
x33=45.5534044627264x_{33} = 45.5534044627264
x33=76.9691283508747x_{33} = 76.9691283508747
Decreasing at intervals
[98.9602340090719,∞)\left[98.9602340090719, \infty\right)
Increasing at intervals
(−∞,−98.9602340090719]\left(-\infty, -98.9602340090719\right]
Inflection points
Let's find the inflection points, we'll need to solve the equation for this
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(the second derivative equals zero),
the roots of this equation will be the inflection points for the specified function graph:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
the second derivative
−2xsin⁡(x)(x2+1)2−sin⁡(x)atan⁡(x)+2cos⁡(x)x2+1=0- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1} = 0
Solve this equation
The roots of this equation
x1=−28.2759609016006x_{1} = -28.2759609016006
x2=21.9938531789562x_{2} = 21.9938531789562
x3=−18.8532519435147x_{3} = -18.8532519435147
x4=15.7133138949299x_{4} = 15.7133138949299
x5=−72.256877018428x_{5} = -72.256877018428
x6=75.3984495204372x_{6} = 75.3984495204372
x7=18.8532519435147x_{7} = 18.8532519435147
x8=−21.9938531789562x_{8} = -21.9938531789562
x9=43.9829646343884x_{9} = 43.9829646343884
x10=87.9647600263064x_{10} = 87.9647600263064
x11=−53.4075267137478x_{11} = -53.4075267137478
x12=−87.9647600263064x_{12} = -87.9647600263064
x13=−56.5490703302555x_{13} = -56.5490703302555
x14=−81.6816012996122x_{14} = -81.6816012996122
x15=65.9737410345762x_{15} = 65.9737410345762
x16=56.5490703302555x_{16} = 56.5490703302555
x17=40.8414794224676x_{17} = 40.8414794224676
x18=78.5400244008501x_{18} = 78.5400244008501
x19=72.256877018428x_{19} = 72.256877018428
x20=−43.9829646343884x_{20} = -43.9829646343884
x21=31.4172417711937x_{21} = 31.4172417711937
x22=3.27025559384994x_{22} = 3.27025559384994
x23=−94.2479239057106x_{23} = -94.2479239057106
x24=−15.7133138949299x_{24} = -15.7133138949299
x25=−3.27025559384994x_{25} = -3.27025559384994
x26=84.8231799223075x_{26} = 84.8231799223075
x27=−12.5747920390384x_{27} = -12.5747920390384
x28=−37.7000223964691x_{28} = -37.7000223964691
x29=−97.3895073712924x_{29} = -97.3895073712924
x30=−50.2659926334542x_{30} = -50.2659926334542
x31=−84.8231799223075x_{31} = -84.8231799223075
x32=−78.5400244008501x_{32} = -78.5400244008501
x33=12.5747920390384x_{33} = 12.5747920390384
x34=−25.134805522921x_{34} = -25.134805522921
x35=−59.690621520068x_{35} = -59.690621520068
x36=28.2759609016006x_{36} = 28.2759609016006
x37=−31.4172417711937x_{37} = -31.4172417711937
x38=−75.3984495204372x_{38} = -75.3984495204372
x39=62.8321788004678x_{39} = 62.8321788004678
x40=37.7000223964691x_{40} = 37.7000223964691
x41=6.31756549582733x_{41} = 6.31756549582733
x42=147.654913369085x_{42} = 147.654913369085
x43=69.1153073388908x_{43} = 69.1153073388908
x44=−47.1244707319001x_{44} = -47.1244707319001
x45=91.1063414102081x_{45} = 91.1063414102081
x46=0.777864066729225x_{46} = 0.777864066729225
x47=−100.531091687256x_{47} = -100.531091687256
x48=34.558604347829x_{48} = 34.558604347829
x49=100.531091687256x_{49} = 100.531091687256
x50=−62.8321788004678x_{50} = -62.8321788004678
x51=97.3895073712924x_{51} = 97.3895073712924
x52=−65.9737410345762x_{52} = -65.9737410345762
x53=59.690621520068x_{53} = 59.690621520068
x54=25.134805522921x_{54} = 25.134805522921
x55=53.4075267137478x_{55} = 53.4075267137478
x56=−34.558604347829x_{56} = -34.558604347829
x57=81.6816012996122x_{57} = 81.6816012996122
x58=50.2659926334542x_{58} = 50.2659926334542
x59=−40.8414794224676x_{59} = -40.8414794224676
x60=9.43990010438496x_{60} = 9.43990010438496
x61=−6.31756549582733x_{61} = -6.31756549582733
x62=94.2479239057106x_{62} = 94.2479239057106
x63=47.1244707319001x_{63} = 47.1244707319001
x64=−9.43990010438496x_{64} = -9.43990010438496
x65=−69.1153073388908x_{65} = -69.1153073388908
x66=−91.1063414102081x_{66} = -91.1063414102081
x67=−103.672676751813x_{67} = -103.672676751813

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
[147.654913369085,∞)\left[147.654913369085, \infty\right)
Convex at the intervals
(−∞,−100.531091687256]\left(-\infty, -100.531091687256\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(sin⁡(x)atan⁡(x))=⟨−12,12⟩π\lim_{x \to -\infty}\left(\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=⟨−12,12⟩πy = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
lim⁡x→∞(sin⁡(x)atan⁡(x))=⟨−12,12⟩π\lim_{x \to \infty}\left(\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}\right) = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=⟨−12,12⟩πy = \left\langle - \frac{1}{2}, \frac{1}{2}\right\rangle \pi
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of sin(x)*atan(x), divided by x at x->+oo and x ->-oo
lim⁡x→−∞(sin⁡(x)atan⁡(x)x)=0\lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(sin⁡(x)atan⁡(x)x)=0\lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \operatorname{atan}{\left(x \right)}}{x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the left
Even and odd functions
Let's check, whether the function even or odd by using relations f = f(-x) и f = -f(-x).
So, check:
sin⁡(x)atan⁡(x)=sin⁡(x)atan⁡(x)\sin{\left(x \right)} \operatorname{atan}{\left(x \right)} = \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}
- No
sin⁡(x)atan⁡(x)=−sin⁡(x)atan⁡(x)\sin{\left(x \right)} \operatorname{atan}{\left(x \right)} = - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}
- No
so, the function
not is
neither even, nor odd
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