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Plotting a function graph/ cot(2*x)*tan(7*x)

Graphing y = cot(2*x)*tan(7*x)

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The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
f(x) = cot(2*x)*tan(7*x)
f(x)=tan⁡(7x)cot⁡(2x)f{\left(x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)} 
f = tan(7*x)*cot(2*x)
The graph of the function
02468-8-6-4-2-1010-500500
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:
tan⁡(7x)cot⁡(2x)=0\tan{\left(7 x \right)} \cot{\left(2 x \right)} = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=−71.8078320820524x_{1} = -71.8078320820524
x2=−75.8470226366679x_{2} = -75.8470226366679
x3=−38.484510006475x_{3} = -38.484510006475
x4=−9.87357691128221x_{4} = -9.87357691128221
x5=−48.0214877048726x_{5} = -48.0214877048726
x6=4.03919055461545x_{6} = 4.03919055461545
x7=−27.8255349317953x_{7} = -27.8255349317953
x8=−70.0126362800011x_{8} = -70.0126362800011
x9=36.9137136796801x_{9} = 36.9137136796801
x10=56.0998688141035x_{10} = 56.0998688141035
x11=−31.8647254864108x_{11} = -31.8647254864108
x12=−4.03919055461545x_{12} = -4.03919055461545
x13=−52.060678259488x_{13} = -52.060678259488
x14=−41.738302397693x_{14} = -41.738302397693
x15=−13.9127674658977x_{15} = -13.9127674658977
x16=100.082165964361x_{16} = 100.082165964361
x17=59.2414614676932x_{17} = 59.2414614676932
x18=−92.0037848551297x_{18} = -92.0037848551297
x19=70.0126362800011x_{19} = 70.0126362800011
x20=−39.9431065956417x_{20} = -39.9431065956417
x21=−79.4374142407705x_{21} = -79.4374142407705
x22=42.1871013482058x_{22} = 42.1871013482058
x23=−23.7863443771799x_{23} = -23.7863443771799
x24=8.63937979737193x_{24} = 8.63937979737193
x25=17.9519580205131x_{25} = 17.9519580205131
x26=64.6270488738472x_{26} = 64.6270488738472
x27=74.0518268346165x_{27} = 74.0518268346165
x28=34.1087202389749x_{28} = 34.1087202389749
x29=48.0214877048726x_{29} = 48.0214877048726
x30=46.2262919028212x_{30} = 46.2262919028212
x31=26.030339129744x_{31} = 26.030339129744
x32=−45.7774929523084x_{32} = -45.7774929523084
x33=−55.7632696012188x_{33} = -55.7632696012188
x34=−74.0518268346165x_{34} = -74.0518268346165
x35=16.1567622184618x_{35} = 16.1567622184618
x36=−96.0429754097451x_{36} = -96.0429754097451
x37=−5.83438635666676x_{37} = -5.83438635666676
x38=2.24399475256414x_{38} = 2.24399475256414
x39=−26.030339129744x_{39} = -26.030339129744
x40=−22.4399475256414x_{40} = -22.4399475256414
x41=−77.7544181763474x_{41} = -77.7544181763474
x42=93.4623814442964x_{42} = 93.4623814442964
x43=82.1302079438475x_{43} = 82.1302079438475
x44=−53.8558740615393x_{44} = -53.8558740615393
x45=−35.9039160410262x_{45} = -35.9039160410262
x46=86.1693984984629x_{46} = 86.1693984984629
x47=61.9342551707702x_{47} = 61.9342551707702
x48=38.484510006475x_{48} = 38.484510006475
x49=39.9431065956417x_{49} = 39.9431065956417
x50=68.2174404779498x_{50} = 68.2174404779498
x51=−97.8381712117964x_{51} = -97.8381712117964
x52=60.1390593687189x_{52} = 60.1390593687189
x53=98.2869701623092x_{53} = 98.2869701623092
x54=64.1782499233343x_{54} = 64.1782499233343
x55=−87.5157953500014x_{55} = -87.5157953500014
x56=−85.7205995479501x_{56} = -85.7205995479501
x57=92.0037848551297x_{57} = 92.0037848551297
x58=12.1175716638463x_{58} = 12.1175716638463
x59=−8.0783811092309x_{59} = -8.0783811092309
x60=78.091017389232x_{60} = 78.091017389232
x61=−89.7597901025655x_{61} = -89.7597901025655
x62=−63.7294509728215x_{62} = -63.7294509728215
x63=35.4551170905134x_{63} = 35.4551170905134
x64=20.1959527730772x_{64} = 20.1959527730772
x65=76.2958215871807x_{65} = 76.2958215871807
x66=52.060678259488x_{66} = 52.060678259488
x67=32.3135244369236x_{67} = 32.3135244369236
x68=−57.8950646161548x_{68} = -57.8950646161548
x69=−99.7455667514759x_{69} = -99.7455667514759
x70=24.2351433276927x_{70} = 24.2351433276927
x71=−62.0464549083984x_{71} = -62.0464549083984
x72=−33.7721210260903x_{72} = -33.7721210260903
x73=−1.79519580205131x_{73} = -1.79519580205131
x74=−19.7471538225644x_{74} = -19.7471538225644
x75=30.0695296843594x_{75} = 30.0695296843594
x76=−30.0695296843594x_{76} = -30.0695296843594
x77=−58.7926625171804x_{77} = -58.7926625171804
x78=−46.2262919028212x_{78} = -46.2262919028212
x79=80.3350121417961x_{79} = 80.3350121417961
x80=90.2085890530783x_{80} = 90.2085890530783
x81=50.7142814079495x_{81} = 50.7142814079495
x82=−83.9254037458988x_{82} = -83.9254037458988
x83=38.1479107935903x_{83} = 38.1479107935903
x84=−65.07584782436x_{84} = -65.07584782436
x85=96.0429754097451x_{85} = 96.0429754097451
x86=10.322375861795x_{86} = 10.322375861795
x87=−11.7809724509617x_{87} = -11.7809724509617
x88=−17.9519580205131x_{88} = -17.9519580205131
x89=−49.8166835069239x_{89} = -49.8166835069239
x90=83.9254037458988x_{90} = 83.9254037458988
x91=21.5423496246157x_{91} = 21.5423496246157
x92=73.1542289335909x_{92} = 73.1542289335909
x93=−67.768641527437x_{93} = -67.768641527437
x94=−93.798980657181x_{94} = -93.798980657181
x95=−79.8862131912833x_{95} = -79.8862131912833
x96=54.3046730120521x_{96} = 54.3046730120521
x97=8.0783811092309x_{97} = 8.0783811092309
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to cot(2*x)*tan(7*x).
tan⁡(0⋅7)cot⁡(0⋅2)\tan{\left(0 \cdot 7 \right)} \cot{\left(0 \cdot 2 \right)}
The result:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- the solutions of the equation d'not exist
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
True

Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=lim⁡x→−∞(tan⁡(7x)cot⁡(2x))y = \lim_{x \to -\infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞(tan⁡(7x)cot⁡(2x))y = \lim_{x \to \infty}\left(\tan{\left(7 x \right)} \cot{\left(2 x \right)}\right)
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of cot(2*x)*tan(7*x), divided by x at x->+oo and x ->-oo
True

Let's take the limit
so,
inclined asymptote equation on the left:
y=xlim⁡x→−∞(tan⁡(7x)cot⁡(2x)x)y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(tan⁡(7x)cot⁡(2x)x)y = x \lim_{x \to \infty}\left(\frac{\tan{\left(7 x \right)} \cot{\left(2 x \right)}}{x}\right)
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:
tan⁡(7x)cot⁡(2x)=tan⁡(7x)cot⁡(2x)\tan{\left(7 x \right)} \cot{\left(2 x \right)} = \tan{\left(7 x \right)} \cot{\left(2 x \right)}
- Yes
tan⁡(7x)cot⁡(2x)=−tan⁡(7x)cot⁡(2x)\tan{\left(7 x \right)} \cot{\left(2 x \right)} = - \tan{\left(7 x \right)} \cot{\left(2 x \right)}
- No
so, the function
is
even
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