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Trazado el gráfico de la función/ cos(x)*cos(sin(x))

Gráfico de la función y = cos(x)*cos(sin(x))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = cos(x)*cos(sin(x))
f(x)=cos⁡(x)cos⁡(sin⁡(x))f{\left(x \right)} = \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} 
f = cos(x)*cos(sin(x))
Gráfico de la función
02468-8-6-4-2-10102-2
Puntos de cruce con el eje de coordenadas X
El gráfico de la función cruce el eje X con f = 0
o sea hay que resolver la ecuación:
cos⁡(x)cos⁡(sin⁡(x))=0\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π2x_{1} = - \frac{\pi}{2}
x2=π2x_{2} = \frac{\pi}{2}
Solución numérica
x1=−29.845130209103x_{1} = -29.845130209103
x2=−67.5442420521806x_{2} = -67.5442420521806
x3=−70.6858347057703x_{3} = -70.6858347057703
x4=64.4026493985908x_{4} = 64.4026493985908
x5=−36.1283155162826x_{5} = -36.1283155162826
x6=−92.6769832808989x_{6} = -92.6769832808989
x7=−61.261056745001x_{7} = -61.261056745001
x8=−76.9690200129499x_{8} = -76.9690200129499
x9=−98.9601685880785x_{9} = -98.9601685880785
x10=−95.8185759344887x_{10} = -95.8185759344887
x11=29.845130209103x_{11} = 29.845130209103
x12=80.1106126665397x_{12} = 80.1106126665397
x13=−64.4026493985908x_{13} = -64.4026493985908
x14=36.1283155162826x_{14} = 36.1283155162826
x15=73.8274273593601x_{15} = 73.8274273593601
x16=32.9867228626928x_{16} = 32.9867228626928
x17=−4.71238898038469x_{17} = -4.71238898038469
x18=−39.2699081698724x_{18} = -39.2699081698724
x19=26.7035375555132x_{19} = 26.7035375555132
x20=−5244.88893516816x_{20} = -5244.88893516816
x21=95.8185759344887x_{21} = 95.8185759344887
x22=−7.85398163397448x_{22} = -7.85398163397448
x23=−17.2787595947439x_{23} = -17.2787595947439
x24=−10.9955742875643x_{24} = -10.9955742875643
x25=98.9601685880785x_{25} = 98.9601685880785
x26=−86.3937979737193x_{26} = -86.3937979737193
x27=92.6769832808989x_{27} = 92.6769832808989
x28=−48.6946861306418x_{28} = -48.6946861306418
x29=54.9778714378214x_{29} = 54.9778714378214
x30=45.553093477052x_{30} = 45.553093477052
x31=23.5619449019235x_{31} = 23.5619449019235
x32=76.9690200129499x_{32} = 76.9690200129499
x33=−89.5353906273091x_{33} = -89.5353906273091
x34=4.71238898038469x_{34} = 4.71238898038469
x35=−26.7035375555132x_{35} = -26.7035375555132
x36=−80.1106126665397x_{36} = -80.1106126665397
x37=7.85398163397448x_{37} = 7.85398163397448
x38=14.1371669411541x_{38} = 14.1371669411541
x39=86.3937979737193x_{39} = 86.3937979737193
x40=−45.553093477052x_{40} = -45.553093477052
x41=−83.2522053201295x_{41} = -83.2522053201295
x42=70.6858347057703x_{42} = 70.6858347057703
x43=83.2522053201295x_{43} = 83.2522053201295
x44=48.6946861306418x_{44} = 48.6946861306418
x45=−20.4203522483337x_{45} = -20.4203522483337
x46=51.8362787842316x_{46} = 51.8362787842316
x47=10.9955742875643x_{47} = 10.9955742875643
x48=20.4203522483337x_{48} = 20.4203522483337
x49=1.5707963267949x_{49} = 1.5707963267949
x50=89.5353906273091x_{50} = 89.5353906273091
x51=17.2787595947439x_{51} = 17.2787595947439
x52=58.1194640914112x_{52} = 58.1194640914112
x53=61.261056745001x_{53} = 61.261056745001
x54=−51.8362787842316x_{54} = -51.8362787842316
x55=−32.9867228626928x_{55} = -32.9867228626928
x56=−14.1371669411541x_{56} = -14.1371669411541
x57=−58.1194640914112x_{57} = -58.1194640914112
x58=−42.4115008234622x_{58} = -42.4115008234622
x59=−54.9778714378214x_{59} = -54.9778714378214
x60=−1.5707963267949x_{60} = -1.5707963267949
x61=42.4115008234622x_{61} = 42.4115008234622
x62=39.2699081698724x_{62} = 39.2699081698724
x63=67.5442420521806x_{63} = 67.5442420521806
x64=−23.5619449019235x_{64} = -23.5619449019235
x65=−73.8274273593601x_{65} = -73.8274273593601
Puntos de cruce con el eje de coordenadas Y
El gráfico cruce el eje Y cuando x es igual a 0:
sustituimos x = 0 en cos(x)*cos(sin(x)).
cos⁡(0)cos⁡(sin⁡(0))\cos{\left(0 \right)} \cos{\left(\sin{\left(0 \right)} \right)}
Resultado:
f(0)=1f{\left(0 \right)} = 1
Punto:
(0, 1)
Extremos de la función
Para hallar los extremos hay que resolver la ecuación
ddxf(x)=0\frac{d}{d x} f{\left(x \right)} = 0
(la derivada es igual a cero),
y las raíces de esta ecuación serán los extremos de esta función:
ddxf(x)=\frac{d}{d x} f{\left(x \right)} =
primera derivada
−sin⁡(x)cos⁡(sin⁡(x))−sin⁡(sin⁡(x))cos⁡2(x)=0- \sin{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} - \sin{\left(\sin{\left(x \right)} \right)} \cos^{2}{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=62.8318530717959x_{1} = 62.8318530717959
x2=−50.2654824574367x_{2} = -50.2654824574367
x3=84.8230016469244x_{3} = 84.8230016469244
x4=−53.4070751110265x_{4} = -53.4070751110265
x5=−84.8230016469244x_{5} = -84.8230016469244
x6=−3.14159265358979x_{6} = -3.14159265358979
x7=−6.28318530717959x_{7} = -6.28318530717959
x8=2899.69001926338x_{8} = 2899.69001926338
x9=78.5398163397448x_{9} = 78.5398163397448
x10=−75.398223686155x_{10} = -75.398223686155
x11=−9.42477796076938x_{11} = -9.42477796076938
x12=72.2566310325652x_{12} = 72.2566310325652
x13=−43.9822971502571x_{13} = -43.9822971502571
x14=40.8407044966673x_{14} = 40.8407044966673
x15=−69.1150383789755x_{15} = -69.1150383789755
x16=12.5663706143592x_{16} = 12.5663706143592
x17=87.9645943005142x_{17} = 87.9645943005142
x18=59.6902604182061x_{18} = 59.6902604182061
x19=−37.6991118430775x_{19} = -37.6991118430775
x20=−91.106186954104x_{20} = -91.106186954104
x21=97.3893722612836x_{21} = 97.3893722612836
x22=0x_{22} = 0
x23=18.8495559215388x_{23} = 18.8495559215388
x24=−78.5398163397448x_{24} = -78.5398163397448
x25=34.5575191894877x_{25} = 34.5575191894877
x26=−94.2477796076938x_{26} = -94.2477796076938
x27=2582.38916125081x_{27} = 2582.38916125081
x28=43.9822971502571x_{28} = 43.9822971502571
x29=153.9380400259x_{29} = 153.9380400259
x30=−31.4159265358979x_{30} = -31.4159265358979
x31=−81.6814089933346x_{31} = -81.6814089933346
x32=−65.9734457253857x_{32} = -65.9734457253857
x33=56.5486677646163x_{33} = 56.5486677646163
x34=3.14159265358979x_{34} = 3.14159265358979
x35=15.707963267949x_{35} = 15.707963267949
x36=−21.9911485751286x_{36} = -21.9911485751286
x37=50.2654824574367x_{37} = 50.2654824574367
x38=−15.707963267949x_{38} = -15.707963267949
x39=28.2743338823081x_{39} = 28.2743338823081
x40=94.2477796076938x_{40} = 94.2477796076938
x41=−2199.11485751286x_{41} = -2199.11485751286
x42=−59.6902604182061x_{42} = -59.6902604182061
x43=−62.8318530717959x_{43} = -62.8318530717959
x44=−34.5575191894877x_{44} = -34.5575191894877
x45=−97.3893722612836x_{45} = -97.3893722612836
x46=21.9911485751286x_{46} = 21.9911485751286
x47=65.9734457253857x_{47} = 65.9734457253857
x48=37.6991118430775x_{48} = 37.6991118430775
x49=−87.9645943005142x_{49} = -87.9645943005142
x50=−72.2566310325652x_{50} = -72.2566310325652
x51=−25.1327412287183x_{51} = -25.1327412287183
x52=−28.2743338823081x_{52} = -28.2743338823081
x53=81.6814089933346x_{53} = 81.6814089933346
x54=6.28318530717959x_{54} = 6.28318530717959
x55=100.530964914873x_{55} = 100.530964914873
x56=−47.1238898038469x_{56} = -47.1238898038469
Signos de extremos en los puntos:
(62.83185307179586, 1)

(-50.26548245743669, 1)

(84.82300164692441, -1)

(-53.40707511102649, -1)

(-84.82300164692441, -1)

(-3.141592653589793, -1)

(-6.283185307179586, 1)

(2899.6900192633793, -1)

(78.53981633974483, -1)

(-75.39822368615503, 1)

(-9.42477796076938, -1)

(72.25663103256524, -1)

(-43.982297150257104, 1)

(40.840704496667314, -1)

(-69.11503837897546, 1)

(12.566370614359172, 1)

(87.96459430051421, 1)

(59.69026041820607, -1)

(-37.69911184307752, 1)

(-91.106186954104, -1)

(97.3893722612836, -1)

(0, 1)

(18.84955592153876, 1)

(-78.53981633974483, -1)

(34.55751918948773, -1)

(-94.2477796076938, 1)

(2582.38916125081, 1)

(43.982297150257104, 1)

(153.93804002589988, -1)

(-31.41592653589793, 1)

(-81.68140899333463, 1)

(-65.97344572538566, -1)

(56.548667764616276, 1)

(3.141592653589793, -1)

(15.707963267948966, -1)

(-21.991148575128552, -1)

(50.26548245743669, 1)

(-15.707963267948966, -1)

(28.274333882308138, -1)

(94.2477796076938, 1)

(-2199.1148575128555, 1)

(-59.69026041820607, -1)

(-62.83185307179586, 1)

(-34.55751918948773, -1)

(-97.3893722612836, -1)

(21.991148575128552, -1)

(65.97344572538566, -1)

(37.69911184307752, 1)

(-87.96459430051421, 1)

(-72.25663103256524, -1)

(-25.132741228718345, 1)

(-28.274333882308138, -1)

(81.68140899333463, 1)

(6.283185307179586, 1)

(100.53096491487338, 1)

(-47.1238898038469, -1)


Intervalos de crecimiento y decrecimiento de la función:
Hallemos los intervalos donde la función crece y decrece y también los puntos mínimos y máximos de la función, para lo cual miramos cómo se comporta la función en los extremos con desviación mínima del extremo:
Puntos mínimos de la función:
x1=84.8230016469244x_{1} = 84.8230016469244
x2=−53.4070751110265x_{2} = -53.4070751110265
x3=−84.8230016469244x_{3} = -84.8230016469244
x4=−3.14159265358979x_{4} = -3.14159265358979
x5=2899.69001926338x_{5} = 2899.69001926338
x6=78.5398163397448x_{6} = 78.5398163397448
x7=−9.42477796076938x_{7} = -9.42477796076938
x8=72.2566310325652x_{8} = 72.2566310325652
x9=40.8407044966673x_{9} = 40.8407044966673
x10=59.6902604182061x_{10} = 59.6902604182061
x11=−91.106186954104x_{11} = -91.106186954104
x12=97.3893722612836x_{12} = 97.3893722612836
x13=−78.5398163397448x_{13} = -78.5398163397448
x14=34.5575191894877x_{14} = 34.5575191894877
x15=153.9380400259x_{15} = 153.9380400259
x16=−65.9734457253857x_{16} = -65.9734457253857
x17=3.14159265358979x_{17} = 3.14159265358979
x18=15.707963267949x_{18} = 15.707963267949
x19=−21.9911485751286x_{19} = -21.9911485751286
x20=−15.707963267949x_{20} = -15.707963267949
x21=28.2743338823081x_{21} = 28.2743338823081
x22=−59.6902604182061x_{22} = -59.6902604182061
x23=−34.5575191894877x_{23} = -34.5575191894877
x24=−97.3893722612836x_{24} = -97.3893722612836
x25=21.9911485751286x_{25} = 21.9911485751286
x26=65.9734457253857x_{26} = 65.9734457253857
x27=−72.2566310325652x_{27} = -72.2566310325652
x28=−28.2743338823081x_{28} = -28.2743338823081
x29=−47.1238898038469x_{29} = -47.1238898038469
Puntos máximos de la función:
x29=62.8318530717959x_{29} = 62.8318530717959
x29=−50.2654824574367x_{29} = -50.2654824574367
x29=−6.28318530717959x_{29} = -6.28318530717959
x29=−75.398223686155x_{29} = -75.398223686155
x29=−43.9822971502571x_{29} = -43.9822971502571
x29=−69.1150383789755x_{29} = -69.1150383789755
x29=12.5663706143592x_{29} = 12.5663706143592
x29=87.9645943005142x_{29} = 87.9645943005142
x29=−37.6991118430775x_{29} = -37.6991118430775
x29=0x_{29} = 0
x29=18.8495559215388x_{29} = 18.8495559215388
x29=−94.2477796076938x_{29} = -94.2477796076938
x29=2582.38916125081x_{29} = 2582.38916125081
x29=43.9822971502571x_{29} = 43.9822971502571
x29=−31.4159265358979x_{29} = -31.4159265358979
x29=−81.6814089933346x_{29} = -81.6814089933346
x29=56.5486677646163x_{29} = 56.5486677646163
x29=50.2654824574367x_{29} = 50.2654824574367
x29=94.2477796076938x_{29} = 94.2477796076938
x29=−2199.11485751286x_{29} = -2199.11485751286
x29=−62.8318530717959x_{29} = -62.8318530717959
x29=37.6991118430775x_{29} = 37.6991118430775
x29=−87.9645943005142x_{29} = -87.9645943005142
x29=−25.1327412287183x_{29} = -25.1327412287183
x29=81.6814089933346x_{29} = 81.6814089933346
x29=6.28318530717959x_{29} = 6.28318530717959
x29=100.530964914873x_{29} = 100.530964914873
Decrece en los intervalos
[2899.69001926338,∞)\left[2899.69001926338, \infty\right)
Crece en los intervalos
(−∞,−97.3893722612836]\left(-\infty, -97.3893722612836\right]
Puntos de flexiones
Hallemos los puntos de flexiones, para eso hay que resolver la ecuación
d2dx2f(x)=0\frac{d^{2}}{d x^{2}} f{\left(x \right)} = 0
(la segunda derivada es igual a cero),
las raíces de la ecuación obtenida serán los puntos de flexión para el gráfico de la función indicado:
d2dx2f(x)=\frac{d^{2}}{d x^{2}} f{\left(x \right)} =
segunda derivada
(3sin⁡(x)sin⁡(sin⁡(x))−cos⁡2(x)cos⁡(sin⁡(x))−cos⁡(sin⁡(x)))cos⁡(x)=0\left(3 \sin{\left(x \right)} \sin{\left(\sin{\left(x \right)} \right)} - \cos^{2}{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} - \cos{\left(\sin{\left(x \right)} \right)}\right) \cos{\left(x \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=3.86780572583686x_{1} = 3.86780572583686
x2=60.4164734904531x_{2} = 60.4164734904531
x3=−29.845130209103x_{3} = -29.845130209103
x4=50.9916955296838x_{4} = 50.9916955296838
x5=−82.4076220655817x_{5} = -82.4076220655817
x6=−10.1509910330164x_{6} = -10.1509910330164
x7=−19.5757689937858x_{7} = -19.5757689937858
x8=29.845130209103x_{8} = 29.845130209103
x9=−93.5215665354467x_{9} = -93.5215665354467
x10=95.8185759344887x_{10} = 95.8185759344887
x11=−84.0967885746773x_{11} = -84.0967885746773
x12=−77.8136032674978x_{12} = -77.8136032674978
x13=−5.55697223493252x_{13} = -5.55697223493252
x14=−85.5492147191715x_{14} = -85.5492147191715
x15=62.1056399995488x_{15} = 62.1056399995488
x16=54.1332881832735x_{16} = 54.1332881832735
x17=−41.5669175689144x_{17} = -41.5669175689144
x18=70.6858347057703x_{18} = 70.6858347057703
x19=−76.1244367584021x_{19} = -76.1244367584021
x20=−49.5392693851896x_{20} = -49.5392693851896
x21=−14.1371669411541x_{21} = -14.1371669411541
x22=42.4115008234622x_{22} = 42.4115008234622
x23=−40.1144914244202x_{23} = -40.1144914244202
x24=47.850102876094x_{24} = 47.850102876094
x25=−3.86780572583686x_{25} = -3.86780572583686
x26=−60.4164734904531x_{26} = -60.4164734904531
x27=33.8313061172407x_{27} = 33.8313061172407
x28=99.8047518426263x_{28} = 99.8047518426263
x29=84.0967885746773x_{29} = 84.0967885746773
x30=−80.1106126665397x_{30} = -80.1106126665397
x31=55.8224546923692x_{31} = 55.8224546923692
x32=76.1244367584021x_{32} = 76.1244367584021
x33=−32.142139608145x_{33} = -32.142139608145
x34=−54.1332881832735x_{34} = -54.1332881832735
x35=48.6946861306418x_{35} = 48.6946861306418
x36=46.3976767315998x_{36} = 46.3976767315998
x37=−20.4203522483337x_{37} = -20.4203522483337
x38=10.1509910330164x_{38} = 10.1509910330164
x39=20.4203522483337x_{39} = 20.4203522483337
x40=40.1144914244202x_{40} = 40.1144914244202
x41=11.8401575421121x_{41} = 11.8401575421121
x42=90.3799738818569x_{42} = 90.3799738818569
x43=77.8136032674978x_{43} = 77.8136032674978
x44=−71.5304179603182x_{44} = -71.5304179603182
x45=2.41537958134273x_{45} = 2.41537958134273
x46=32.142139608145x_{46} = 32.142139608145
x47=−73.8274273593601x_{47} = -73.8274273593601
x48=−67.5442420521806x_{48} = -67.5442420521806
x49=98.1155853335307x_{49} = 98.1155853335307
x50=−36.1283155162826x_{50} = -36.1283155162826
x51=−27.5481208100611x_{51} = -27.5481208100611
x52=82.4076220655817x_{52} = 82.4076220655817
x53=36.1283155162826x_{53} = 36.1283155162826
x54=16.434176340196x_{54} = 16.434176340196
x55=26.7035375555132x_{55} = 26.7035375555132
x56=−18.1233428492917x_{56} = -18.1233428492917
x57=−89.5353906273091x_{57} = -89.5353906273091
x58=−91.8324000263511x_{58} = -91.8324000263511
x59=−99.8047518426263x_{59} = -99.8047518426263
x60=7.85398163397448x_{60} = 7.85398163397448
x61=14.1371669411541x_{61} = 14.1371669411541
x62=86.3937979737193x_{62} = 86.3937979737193
x63=18.1233428492917x_{63} = 18.1233428492917
x64=−55.8224546923692x_{64} = -55.8224546923692
x65=51.8362787842316x_{65} = 51.8362787842316
x66=−51.8362787842316x_{66} = -51.8362787842316
x67=−33.8313061172407x_{67} = -33.8313061172407
x68=−38.4253249153246x_{68} = -38.4253249153246
x69=5.55697223493252x_{69} = 5.55697223493252
x70=25.8589543009654x_{70} = 25.8589543009654
x71=−1.5707963267949x_{71} = -1.5707963267949
x72=24.4065281564713x_{72} = 24.4065281564713
x73=−23.5619449019235x_{73} = -23.5619449019235
x74=−16.434176340196x_{74} = -16.434176340196
x75=69.8412514512225x_{75} = 69.8412514512225
x76=64.4026493985908x_{76} = 64.4026493985908
x77=−62.1056399995488x_{77} = -62.1056399995488
x78=−47.850102876094x_{78} = -47.850102876094
x79=38.4253249153246x_{79} = 38.4253249153246
x80=−95.8185759344887x_{80} = -95.8185759344887
x81=−98.1155853335307x_{81} = -98.1155853335307
x82=80.1106126665397x_{82} = 80.1106126665397
x83=−64.4026493985908x_{83} = -64.4026493985908
x84=88.6908073727613x_{84} = 88.6908073727613
x85=73.8274273593601x_{85} = 73.8274273593601
x86=−11.8401575421121x_{86} = -11.8401575421121
x87=68.3888253067284x_{87} = 68.3888253067284
x88=−7.85398163397448x_{88} = -7.85398163397448
x89=23.5619449019235x_{89} = 23.5619449019235
x90=92.6769832808989x_{90} = 92.6769832808989
x91=91.8324000263511x_{91} = 91.8324000263511
x92=−63.5580661440429x_{92} = -63.5580661440429
x93=−69.8412514512225x_{93} = -69.8412514512225
x94=−45.553093477052x_{94} = -45.553093477052
x95=−25.8589543009654x_{95} = -25.8589543009654
x96=1.5707963267949x_{96} = 1.5707963267949
x97=−58.1194640914112x_{97} = -58.1194640914112
x98=58.1194640914112x_{98} = 58.1194640914112
x99=−42.4115008234622x_{99} = -42.4115008234622

Intervalos de convexidad y concavidad:
Hallemos los intervales donde la función es convexa o cóncava, para eso veamos cómo se comporta la función en los puntos de flexiones:
Cóncava en los intervalos
[92.6769832808989,∞)\left[92.6769832808989, \infty\right)
Convexa en los intervalos
(−∞,−99.8047518426263]\left(-\infty, -99.8047518426263\right]
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞(cos⁡(x)cos⁡(sin⁡(x)))=⟨−1,1⟩\lim_{x \to -\infty}\left(\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
lim⁡x→∞(cos⁡(x)cos⁡(sin⁡(x)))=⟨−1,1⟩\lim_{x \to \infty}\left(\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}\right) = \left\langle -1, 1\right\rangle
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=⟨−1,1⟩y = \left\langle -1, 1\right\rangle
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función cos(x)*cos(sin(x)), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(cos⁡(x)cos⁡(sin⁡(x))x)=0\lim_{x \to -\infty}\left(\frac{\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(cos⁡(x)cos⁡(sin⁡(x))x)=0\lim_{x \to \infty}\left(\frac{\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la izquierda
Paridad e imparidad de la función
Comprobemos si la función es par o impar mediante las relaciones f = f(-x) и f = -f(-x).
Pues, comprobamos:
cos⁡(x)cos⁡(sin⁡(x))=cos⁡(x)cos⁡(sin⁡(x))\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} = \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}
- Sí
cos⁡(x)cos⁡(sin⁡(x))=−cos⁡(x)cos⁡(sin⁡(x))\cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)} = - \cos{\left(x \right)} \cos{\left(\sin{\left(x \right)} \right)}
- No
es decir, función
es
par
    © Sr Examen – Калькулятор