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Plotting a function graph/ abs(sin(x+(pi/3)))

Graphing y = abs(sin(x+(pi/3)))

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [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))
The graph of the function
02468-8-6-4-2-101002
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+π3)∣=0\left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = 0
Solve this equation
The points of intersection with the axis X:

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

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

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

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

                        /                   pi\ 
(60.21385919380437, -sin|60.2138591938044 + --|)
                        \                   3 / 

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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


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:
The function has no minima
Maxima of the function at points:
x66=9.94837673636768x_{66} = 9.94837673636768
x66=−56.025068989018x_{66} = -56.025068989018
x66=57.0722665402146x_{66} = 57.0722665402146
x66=−15.1843644923507x_{66} = -15.1843644923507
x66=60.2138591938044x_{66} = 60.2138591938044
x66=82.2050077689329x_{66} = 82.2050077689329
x66=−37.1755130674792x_{66} = -37.1755130674792
x66=−52.8834763354282x_{66} = -52.8834763354282
x66=85.3466004225227x_{66} = 85.3466004225227
x66=−84.2994028713261x_{66} = -84.2994028713261
x66=−87.4409955249159x_{66} = -87.4409955249159
x66=38.2227106186758x_{66} = 38.2227106186758
x66=−90.5825881785057x_{66} = -90.5825881785057
x66=66.497044500984x_{66} = 66.497044500984
x66=31.9395253114962x_{66} = 31.9395253114962
x66=16.2315620435473x_{66} = 16.2315620435473
x66=22.5147473507269x_{66} = 22.5147473507269
x66=28.7979326579064x_{66} = 28.7979326579064
x66=−24.60914245312x_{66} = -24.60914245312
x66=0.523598775598299x_{66} = 0.523598775598299
x66=−46.6002910282486x_{66} = -46.6002910282486
x66=−78.0162175641465x_{66} = -78.0162175641465
x66=88.4881930761125x_{66} = 88.4881930761125
x66=−68.5914396033772x_{66} = -68.5914396033772
x66=−8.90117918517108x_{66} = -8.90117918517108
x66=13.0899693899575x_{66} = 13.0899693899575
x66=44.5058959258554x_{66} = 44.5058959258554
x66=79.0634151153431x_{66} = 79.0634151153431
x66=−65.4498469497874x_{66} = -65.4498469497874
x66=69.6386371545737x_{66} = 69.6386371545737
x66=−442.440965380563x_{66} = -442.440965380563
x66=19.3731546971371x_{66} = 19.3731546971371
x66=−34.0339204138894x_{66} = -34.0339204138894
x66=−74.8746249105567x_{66} = -74.8746249105567
x66=91.6297857297023x_{66} = 91.6297857297023
x66=−49.7418836818384x_{66} = -49.7418836818384
x66=−2.61799387799149x_{66} = -2.61799387799149
x66=−81.1578102177363x_{66} = -81.1578102177363
x66=6.80678408277789x_{66} = 6.80678408277789
x66=72.7802298081635x_{66} = 72.7802298081635
x66=−43.4586983746588x_{66} = -43.4586983746588
x66=−5.75958653158129x_{66} = -5.75958653158129
x66=−30.8923277602996x_{66} = -30.8923277602996
x66=35.081117965086x_{66} = 35.081117965086
x66=−40.317105721069x_{66} = -40.317105721069
x66=97.9129710368819x_{66} = 97.9129710368819
x66=−96.8657734856853x_{66} = -96.8657734856853
x66=−12.0427718387609x_{66} = -12.0427718387609
x66=−62.3082542961976x_{66} = -62.3082542961976
x66=−93.7241808320955x_{66} = -93.7241808320955
x66=−18.3259571459405x_{66} = -18.3259571459405
x66=101.054563690472x_{66} = 101.054563690472
x66=94.7713783832921x_{66} = 94.7713783832921
x66=53.9306738866248x_{66} = 53.9306738866248
x66=25.6563400043166x_{66} = 25.6563400043166
x66=3.66519142918809x_{66} = 3.66519142918809
x66=−71.733032256967x_{66} = -71.733032256967
x66=−59.1666616426078x_{66} = -59.1666616426078
x66=47.6474885794452x_{66} = 47.6474885794452
x66=−27.7507351067098x_{66} = -27.7507351067098
x66=75.9218224617533x_{66} = 75.9218224617533
x66=41.3643032722656x_{66} = 41.3643032722656
x66=−21.4675497995303x_{66} = -21.4675497995303
x66=−100.007366139275x_{66} = -100.007366139275
x66=50.789081233035x_{66} = 50.789081233035
x66=63.3554518473942x_{66} = 63.3554518473942
Decreasing at intervals
(−∞,−442.440965380563]\left(-\infty, -442.440965380563\right]
Increasing at intervals
[101.054563690472,∞)\left[101.054563690472, \infty\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
−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
Solve this equation
Solutions are not found,
maybe, the function has no inflections
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+π3)∣=∣⟨−1,1⟩∣\lim_{x \to -\infty} \left|{\sin{\left(x + \frac{\pi}{3} \right)}}\right| = \left|{\left\langle -1, 1\right\rangle}\right|
Let's take the limit
so,
equation of the horizontal asymptote on the left:
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|
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=∣⟨−1,1⟩∣y = \left|{\left\langle -1, 1\right\rangle}\right|
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of Abs(sin(x + pi/3)), divided by x at x->+oo and 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
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
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
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+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
so, the function
not is
neither even, nor odd
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