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Trazado el gráfico de la función/ abs(sin(x+(pi/3)))

Gráfico de la función y = abs(sin(x+(pi/3)))

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
       |   /    pi\|
f(x) = |sin|x + --||
       |   \    3 /|
f(x)=∣sin⁡(x+π3)∣f{\left(x \right)} = \left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| 
f = Abs(sin(x + pi/3))
Gráfico de la función
02468-8-6-4-2-101002
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:
∣sin⁡(x+π3)∣=0\left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=−π3x_{1} = - \frac{\pi}{3}
x2=2π3x_{2} = \frac{2 \pi}{3}
Solución numérica
x1=−13.6135681655558x_{1} = -13.6135681655558
x2=−73.3038285837618x_{2} = -73.3038285837618
x3=−10.471975511966x_{3} = -10.471975511966
x4=−98.4365698124802x_{4} = -98.4365698124802
x5=11.5191730631626x_{5} = 11.5191730631626
x6=83.7758040957278x_{6} = 83.7758040957278
x7=58.6430628670095x_{7} = 58.6430628670095
x8=−82.7286065445312x_{8} = -82.7286065445312
x9=−79.5870138909414x_{9} = -79.5870138909414
x10=−89.0117918517108x_{10} = -89.0117918517108
x11=77.4926187885482x_{11} = 77.4926187885482
x12=−26.1799387799149x_{12} = -26.1799387799149
x13=8.37758040957278x_{13} = 8.37758040957278
x14=102.625360017267x_{14} = 102.625360017267
x15=−4.18879020478639x_{15} = -4.18879020478639
x16=−45.0294947014537x_{16} = -45.0294947014537
x17=52.3598775598299x_{17} = 52.3598775598299
x18=27.2271363311115x_{18} = 27.2271363311115
x19=−95.2949771588904x_{19} = -95.2949771588904
x20=−67.0206432765823x_{20} = -67.0206432765823
x21=20.943951023932x_{21} = 20.943951023932
x22=−16.7551608191456x_{22} = -16.7551608191456
x23=5.23598775598299x_{23} = 5.23598775598299
x24=−41.8879020478639x_{24} = -41.8879020478639
x25=−60.7374579694027x_{25} = -60.7374579694027
x26=99.4837673636768x_{26} = 99.4837673636768
x27=74.3510261349584x_{27} = 74.3510261349584
x28=42.9350995990605x_{28} = 42.9350995990605
x29=−48.1710873550435x_{29} = -48.1710873550435
x30=−23.0383461263252x_{30} = -23.0383461263252
x31=64.9262481741891x_{31} = 64.9262481741891
x32=61.7846555205993x_{32} = 61.7846555205993
x33=−35.6047167406843x_{33} = -35.6047167406843
x34=−29.3215314335047x_{34} = -29.3215314335047
x35=36.6519142918809x_{35} = 36.6519142918809
x36=90.0589894029074x_{36} = 90.0589894029074
x37=93.2005820564972x_{37} = 93.2005820564972
x38=−1.0471975511966x_{38} = -1.0471975511966
x39=2229.48358649756x_{39} = 2229.48358649756
x40=96.342174710087x_{40} = 96.342174710087
x41=49.2182849062401x_{41} = 49.2182849062401
x42=80.634211442138x_{42} = 80.634211442138
x43=55.5014702134197x_{43} = 55.5014702134197
x44=−76.4454212373516x_{44} = -76.4454212373516
x45=−32.4631240870945x_{45} = -32.4631240870945
x46=33.5103216382911x_{46} = 33.5103216382911
x47=30.3687289847013x_{47} = 30.3687289847013
x48=39.7935069454707x_{48} = 39.7935069454707
x49=86.9173967493176x_{49} = 86.9173967493176
x50=−70.162235930172x_{50} = -70.162235930172
x51=17.8023583703422x_{51} = 17.8023583703422
x52=14.6607657167524x_{52} = 14.6607657167524
x53=−57.5958653158129x_{53} = -57.5958653158129
x54=−54.4542726622231x_{54} = -54.4542726622231
x55=−51.3126800086333x_{55} = -51.3126800086333
x56=−92.1533845053006x_{56} = -92.1533845053006
x57=71.2094334813686x_{57} = 71.2094334813686
x58=−7.33038285837618x_{58} = -7.33038285837618
x59=−38.7463093942741x_{59} = -38.7463093942741
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 Abs(sin(x + pi/3)).
∣sin⁡(π3)∣\left|{\sin{\left(\frac{\pi}{3} \right)}}\right|
Resultado:
f(0)=32f{\left(0 \right)} = \frac{\sqrt{3}}{2}
Punto:
(0, sqrt(3)/2)
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
cos⁡(x+π3)sign⁡(sin⁡(x+π3))=0\cos{\left(x + \frac{\pi}{3} \right)} \operatorname{sign}{\left(\sin{\left(x + \frac{\pi}{3} \right)} \right)} = 0
Resolvermos esta ecuación
Raíces de esta ecuación
x1=60.2138591938044x_{1} = 60.2138591938044
x2=−18.3259571459405x_{2} = -18.3259571459405
x3=−12.0427718387609x_{3} = -12.0427718387609
x4=44.5058959258554x_{4} = 44.5058959258554
x5=−49.7418836818384x_{5} = -49.7418836818384
x6=−74.8746249105567x_{6} = -74.8746249105567
x7=−78.0162175641465x_{7} = -78.0162175641465
x8=−81.1578102177363x_{8} = -81.1578102177363
x9=−24.60914245312x_{9} = -24.60914245312
x10=−8.90117918517108x_{10} = -8.90117918517108
x11=−96.8657734856853x_{11} = -96.8657734856853
x12=91.6297857297023x_{12} = 91.6297857297023
x13=19.3731546971371x_{13} = 19.3731546971371
x14=53.9306738866248x_{14} = 53.9306738866248
x15=−71.733032256967x_{15} = -71.733032256967
x16=16.2315620435473x_{16} = 16.2315620435473
x17=−40.317105721069x_{17} = -40.317105721069
x18=31.9395253114962x_{18} = 31.9395253114962
x19=41.3643032722656x_{19} = 41.3643032722656
x20=−21.4675497995303x_{20} = -21.4675497995303
x21=−100.007366139275x_{21} = -100.007366139275
x22=63.3554518473942x_{22} = 63.3554518473942
x23=57.0722665402146x_{23} = 57.0722665402146
x24=−15.1843644923507x_{24} = -15.1843644923507
x25=−68.5914396033772x_{25} = -68.5914396033772
x26=72.7802298081635x_{26} = 72.7802298081635
x27=−30.8923277602996x_{27} = -30.8923277602996
x28=−93.7241808320955x_{28} = -93.7241808320955
x29=69.6386371545737x_{29} = 69.6386371545737
x30=22.5147473507269x_{30} = 22.5147473507269
x31=38.2227106186758x_{31} = 38.2227106186758
x32=79.0634151153431x_{32} = 79.0634151153431
x33=−442.440965380563x_{33} = -442.440965380563
x34=−52.8834763354282x_{34} = -52.8834763354282
x35=−46.6002910282486x_{35} = -46.6002910282486
x36=−34.0339204138894x_{36} = -34.0339204138894
x37=101.054563690472x_{37} = 101.054563690472
x38=−59.1666616426078x_{38} = -59.1666616426078
x39=−37.1755130674792x_{39} = -37.1755130674792
x40=3.66519142918809x_{40} = 3.66519142918809
x41=0.523598775598299x_{41} = 0.523598775598299
x42=−27.7507351067098x_{42} = -27.7507351067098
x43=35.081117965086x_{43} = 35.081117965086
x44=−65.4498469497874x_{44} = -65.4498469497874
x45=−43.4586983746588x_{45} = -43.4586983746588
x46=13.0899693899575x_{46} = 13.0899693899575
x47=−5.75958653158129x_{47} = -5.75958653158129
x48=66.497044500984x_{48} = 66.497044500984
x49=6.80678408277789x_{49} = 6.80678408277789
x50=97.9129710368819x_{50} = 97.9129710368819
x51=−90.5825881785057x_{51} = -90.5825881785057
x52=−56.025068989018x_{52} = -56.025068989018
x53=−62.3082542961976x_{53} = -62.3082542961976
x54=85.3466004225227x_{54} = 85.3466004225227
x55=82.2050077689329x_{55} = 82.2050077689329
x56=9.94837673636768x_{56} = 9.94837673636768
x57=94.7713783832921x_{57} = 94.7713783832921
x58=28.7979326579064x_{58} = 28.7979326579064
x59=−87.4409955249159x_{59} = -87.4409955249159
x60=−2.61799387799149x_{60} = -2.61799387799149
x61=88.4881930761125x_{61} = 88.4881930761125
x62=−84.2994028713261x_{62} = -84.2994028713261
x63=50.789081233035x_{63} = 50.789081233035
x64=25.6563400043166x_{64} = 25.6563400043166
x65=47.6474885794452x_{65} = 47.6474885794452
x66=75.9218224617533x_{66} = 75.9218224617533
Signos de extremos en los puntos:
                        /                   pi\ 
(60.21385919380437, -sin|60.2138591938044 + --|)
                        \                   3 / 

                         /                   pi\ 
(-18.32595714594046, -sin|18.3259571459405 - --|)
                         \                   3 / 

                          /                   pi\ 
(-12.042771838760874, -sin|12.0427718387609 - --|)
                          \                   3 / 

                        /                   pi\ 
(44.505895925855405, sin|44.5058959258554 + --|)
                        \                   3 / 

                          /                   pi\ 
(-49.741883681838395, -sin|49.7418836818384 - --|)
                          \                   3 / 

                         /                   pi\ 
(-74.87462491055673, -sin|74.8746249105567 - --|)
                         \                   3 / 

                        /                   pi\ 
(-78.01621756414653, sin|78.0162175641465 - --|)
                        \                   3 / 

                         /                   pi\ 
(-81.15781021773633, -sin|81.1578102177363 - --|)
                         \                   3 / 

                          /                 pi\ 
(-24.609142453120047, -sin|24.60914245312 - --|)
                          \                 3 / 

                        /                   pi\ 
(-8.901179185171081, sin|8.90117918517108 - --|)
                        \                   3 / 

                       /                   pi\ 
(-96.8657734856853, sin|96.8657734856853 - --|)
                       \                   3 / 

                       /                   pi\ 
(91.6297857297023, -sin|91.6297857297023 + --|)
                       \                   3 / 

                        /                   pi\ 
(19.373154697137057, sin|19.3731546971371 + --|)
                        \                   3 / 

                        /                   pi\ 
(53.93067388662478, -sin|53.9306738866248 + --|)
                        \                   3 / 

                        /                  pi\ 
(-71.73303225696695, sin|71.733032256967 - --|)
                        \                  3 / 

                         /                   pi\ 
(16.231562043547264, -sin|16.2315620435473 + --|)
                         \                   3 / 

                        /                  pi\ 
(-40.31710572106901, sin|40.317105721069 - --|)
                        \                  3 / 

                        /                   pi\ 
(31.939525311496233, sin|31.9395253114962 + --|)
                        \                   3 / 

                        /                   pi\ 
(41.36430327226561, -sin|41.3643032722656 + --|)
                        \                   3 / 

                         /                   pi\ 
(-21.467549799530254, sin|21.4675497995303 - --|)
                         \                   3 / 

                          /                   pi\ 
(-100.00736613927508, -sin|100.007366139275 - --|)
                          \                   3 / 

                        /                   pi\ 
(63.355451847394164, sin|63.3554518473942 + --|)
                        \                   3 / 

                       /                   pi\ 
(57.07226654021458, sin|57.0722665402146 + --|)
                       \                   3 / 

                         /                   pi\ 
(-15.184364492350667, sin|15.1843644923507 - --|)
                         \                   3 / 

                         /                   pi\ 
(-68.59143960337715, -sin|68.5914396033772 - --|)
                         \                   3 / 

                        /                   pi\ 
(72.78022980816354, -sin|72.7802298081635 + --|)
                        \                   3 / 

                          /                   pi\ 
(-30.892327760299633, -sin|30.8923277602996 - --|)
                          \                   3 / 

                        /                   pi\ 
(-93.7241808320955, -sin|93.7241808320955 - --|)
                        \                   3 / 

                       /                   pi\ 
(69.63863715457374, sin|69.6386371545737 + --|)
                       \                   3 / 

                        /                   pi\ 
(22.51474735072685, -sin|22.5147473507269 + --|)
                        \                   3 / 

                       /                   pi\ 
(38.22271061867582, sin|38.2227106186758 + --|)
                       \                   3 / 

                        /                   pi\ 
(79.06341511534313, -sin|79.0634151153431 + --|)
                        \                   3 / 

                         /                   pi\ 
(-442.44096538056255, sin|442.440965380563 - --|)
                         \                   3 / 

                         /                   pi\ 
(-52.883476335428185, sin|52.8834763354282 - --|)
                         \                   3 / 

                       /                   pi\ 
(-46.6002910282486, sin|46.6002910282486 - --|)
                       \                   3 / 

                         /                   pi\ 
(-34.033920413889426, sin|34.0339204138894 - --|)
                         \                   3 / 

                        /                   pi\ 
(101.05456369047168, sin|101.054563690472 + --|)
                        \                   3 / 

                        /                   pi\ 
(-59.16666164260777, sin|59.1666616426078 - --|)
                        \                   3 / 

                         /                   pi\ 
(-37.17551306747922, -sin|37.1755130674792 - --|)
                         \                   3 / 

                         /                   pi\ 
(3.6651914291880923, -sin|3.66519142918809 + --|)
                         \                   3 / 

                        /                    pi\ 
(0.5235987755982989, sin|0.523598775598299 + --|)
                        \                    3 / 

                        /                   pi\ 
(-27.75073510670984, sin|27.7507351067098 - --|)
                        \                   3 / 

                        /                  pi\ 
(35.08111796508602, -sin|35.081117965086 + --|)
                        \                  3 / 

                        /                   pi\ 
(-65.44984694978736, sin|65.4498469497874 - --|)
                        \                   3 / 

                         /                   pi\ 
(-43.45869837465881, -sin|43.4586983746588 - --|)
                         \                   3 / 

                        /                   pi\ 
(13.089969389957473, sin|13.0899693899575 + --|)
                        \                   3 / 

                         /                   pi\ 
(-5.759586531581288, -sin|5.75958653158129 - --|)
                         \                   3 / 

                        /                  pi\ 
(66.49704450098396, -sin|66.497044500984 + --|)
                        \                  3 / 

                       /                   pi\ 
(6.806784082777885, sin|6.80678408277789 + --|)
                       \                   3 / 

                        /                   pi\ 
(97.91297103688188, -sin|97.9129710368819 + --|)
                        \                   3 / 

                       /                   pi\ 
(-90.5825881785057, sin|90.5825881785057 - --|)
                       \                   3 / 

                         /                  pi\ 
(-56.02506898901798, -sin|56.025068989018 - --|)
                         \                  3 / 

                         /                   pi\ 
(-62.30825429619757, -sin|62.3082542961976 - --|)
                         \                   3 / 

                        /                   pi\ 
(85.34660042252271, -sin|85.3466004225227 + --|)
                        \                   3 / 

                       /                   pi\ 
(82.20500776893293, sin|82.2050077689329 + --|)
                       \                   3 / 

                       /                   pi\ 
(9.94837673636768, -sin|9.94837673636768 + --|)
                       \                   3 / 

                      /                   pi\ 
(94.7713783832921, sin|94.7713783832921 + --|)
                      \                   3 / 

                         /                   pi\ 
(28.797932657906436, -sin|28.7979326579064 + --|)
                         \                   3 / 

                        /                   pi\ 
(-87.4409955249159, -sin|87.4409955249159 - --|)
                        \                   3 / 

                         /                   pi\ 
(-2.6179938779914944, sin|2.61799387799149 - --|)
                         \                   3 / 

                       /                   pi\ 
(88.48819307611251, sin|88.4881930761125 + --|)
                       \                   3 / 

                        /                   pi\ 
(-84.29940287132612, sin|84.2994028713261 - --|)
                        \                   3 / 

                       /                  pi\ 
(50.78908123303499, sin|50.789081233035 + --|)
                       \                  3 / 

                        /                   pi\ 
(25.656340004316643, sin|25.6563400043166 + --|)
                        \                   3 / 

                         /                   pi\ 
(47.647488579445195, -sin|47.6474885794452 + --|)
                         \                   3 / 

                       /                   pi\ 
(75.92182246175334, sin|75.9218224617533 + --|)
                       \                   3 /


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:
La función no tiene puntos mínimos
Puntos máximos de la función:
x66=60.2138591938044x_{66} = 60.2138591938044
x66=−18.3259571459405x_{66} = -18.3259571459405
x66=−12.0427718387609x_{66} = -12.0427718387609
x66=44.5058959258554x_{66} = 44.5058959258554
x66=−49.7418836818384x_{66} = -49.7418836818384
x66=−74.8746249105567x_{66} = -74.8746249105567
x66=−78.0162175641465x_{66} = -78.0162175641465
x66=−81.1578102177363x_{66} = -81.1578102177363
x66=−24.60914245312x_{66} = -24.60914245312
x66=−8.90117918517108x_{66} = -8.90117918517108
x66=−96.8657734856853x_{66} = -96.8657734856853
x66=91.6297857297023x_{66} = 91.6297857297023
x66=19.3731546971371x_{66} = 19.3731546971371
x66=53.9306738866248x_{66} = 53.9306738866248
x66=−71.733032256967x_{66} = -71.733032256967
x66=16.2315620435473x_{66} = 16.2315620435473
x66=−40.317105721069x_{66} = -40.317105721069
x66=31.9395253114962x_{66} = 31.9395253114962
x66=41.3643032722656x_{66} = 41.3643032722656
x66=−21.4675497995303x_{66} = -21.4675497995303
x66=−100.007366139275x_{66} = -100.007366139275
x66=63.3554518473942x_{66} = 63.3554518473942
x66=57.0722665402146x_{66} = 57.0722665402146
x66=−15.1843644923507x_{66} = -15.1843644923507
x66=−68.5914396033772x_{66} = -68.5914396033772
x66=72.7802298081635x_{66} = 72.7802298081635
x66=−30.8923277602996x_{66} = -30.8923277602996
x66=−93.7241808320955x_{66} = -93.7241808320955
x66=69.6386371545737x_{66} = 69.6386371545737
x66=22.5147473507269x_{66} = 22.5147473507269
x66=38.2227106186758x_{66} = 38.2227106186758
x66=79.0634151153431x_{66} = 79.0634151153431
x66=−442.440965380563x_{66} = -442.440965380563
x66=−52.8834763354282x_{66} = -52.8834763354282
x66=−46.6002910282486x_{66} = -46.6002910282486
x66=−34.0339204138894x_{66} = -34.0339204138894
x66=101.054563690472x_{66} = 101.054563690472
x66=−59.1666616426078x_{66} = -59.1666616426078
x66=−37.1755130674792x_{66} = -37.1755130674792
x66=3.66519142918809x_{66} = 3.66519142918809
x66=0.523598775598299x_{66} = 0.523598775598299
x66=−27.7507351067098x_{66} = -27.7507351067098
x66=35.081117965086x_{66} = 35.081117965086
x66=−65.4498469497874x_{66} = -65.4498469497874
x66=−43.4586983746588x_{66} = -43.4586983746588
x66=13.0899693899575x_{66} = 13.0899693899575
x66=−5.75958653158129x_{66} = -5.75958653158129
x66=66.497044500984x_{66} = 66.497044500984
x66=6.80678408277789x_{66} = 6.80678408277789
x66=97.9129710368819x_{66} = 97.9129710368819
x66=−90.5825881785057x_{66} = -90.5825881785057
x66=−56.025068989018x_{66} = -56.025068989018
x66=−62.3082542961976x_{66} = -62.3082542961976
x66=85.3466004225227x_{66} = 85.3466004225227
x66=82.2050077689329x_{66} = 82.2050077689329
x66=9.94837673636768x_{66} = 9.94837673636768
x66=94.7713783832921x_{66} = 94.7713783832921
x66=28.7979326579064x_{66} = 28.7979326579064
x66=−87.4409955249159x_{66} = -87.4409955249159
x66=−2.61799387799149x_{66} = -2.61799387799149
x66=88.4881930761125x_{66} = 88.4881930761125
x66=−84.2994028713261x_{66} = -84.2994028713261
x66=50.789081233035x_{66} = 50.789081233035
x66=25.6563400043166x_{66} = 25.6563400043166
x66=47.6474885794452x_{66} = 47.6474885794452
x66=75.9218224617533x_{66} = 75.9218224617533
Decrece en los intervalos
(−∞,−442.440965380563]\left(-\infty, -442.440965380563\right]
Crece en los intervalos
[101.054563690472,∞)\left[101.054563690472, \infty\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
−sin⁡(x+π3)sign⁡(sin⁡(x+π3))+2cos⁡2(x+π3)δ(sin⁡(x+π3))=0- \sin{\left(x + \frac{\pi}{3} \right)} \operatorname{sign}{\left(\sin{\left(x + \frac{\pi}{3} \right)} \right)} + 2 \cos^{2}{\left(x + \frac{\pi}{3} \right)} \delta\left(\sin{\left(x + \frac{\pi}{3} \right)}\right) = 0
Resolvermos esta ecuación
Soluciones no halladas,
tal vez la función no tenga flexiones
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
lim⁡x→−∞∣sin⁡(x+π3)∣=∣⟨−1,1⟩∣\lim_{x \to -\infty} \left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = \left|{\left\langle -1, 1\right\rangle}\right|
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=∣⟨−1,1⟩∣y = \left|{\left\langle -1, 1\right\rangle}\right|
lim⁡x→∞∣sin⁡(x+π3)∣=∣⟨−1,1⟩∣\lim_{x \to \infty} \left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = \left|{\left\langle -1, 1\right\rangle}\right|
Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=∣⟨−1,1⟩∣y = \left|{\left\langle -1, 1\right\rangle}\right|
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función Abs(sin(x + pi/3)), dividida por x con x->+oo y x ->-oo
lim⁡x→−∞(∣sin⁡(x+π3)∣x)=0\lim_{x \to -\infty}\left(\frac{\left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right|}{x}\right) = 0
Tomamos como el límite
es decir,
la inclinada coincide con la asíntota horizontal a la derecha
lim⁡x→∞(∣sin⁡(x+π3)∣x)=0\lim_{x \to \infty}\left(\frac{\left|{\sin{\left(x + \frac{\pi}{3} \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:
∣sin⁡(x+π3)∣=−sin⁡(x−π3)cos⁡(x+π6)\left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = \sqrt{- \sin{\left(x - \frac{\pi}{3} \right)} \cos{\left(x + \frac{\pi}{6} \right)}}
- No
∣sin⁡(x+π3)∣=−−sin⁡(x−π3)cos⁡(x+π6)\left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = - \sqrt{- \sin{\left(x - \frac{\pi}{3} \right)} \cos{\left(x + \frac{\pi}{6} \right)}}
- No
es decir, función
no es
par ni impar
    © Sr Examen – Калькулятор