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

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

v

Gráfico:

interior superior

Puntos de intersección:

mostrar?

Definida a trozos:

Solución

Ha introducido [src] 
f(x) = tan(x)*sin(x)
f(x)=sin⁡(x)tan⁡(x)f{\left(x \right)} = \sin{\left(x \right)} \tan{\left(x \right)} 
f = sin(x)*tan(x)
Gráfico de la función
02468-8-6-4-2-1010-100100
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)tan⁡(x)=0\sin{\left(x \right)} \tan{\left(x \right)} = 0
Resolvermos esta ecuación
Puntos de cruce con el eje X:

Solución analítica
x1=0x_{1} = 0
Solución numérica
x1=−59.6902604579627x_{1} = -59.6902604579627
x2=−37.6991118773749x_{2} = -37.6991118773749
x3=12.5663704329274x_{3} = 12.5663704329274
x4=3.14159332506585x_{4} = 3.14159332506585
x5=50.265482446331x_{5} = 50.265482446331
x6=−62.8318524378967x_{6} = -62.8318524378967
x7=−34.5575188250568x_{7} = -34.5575188250568
x8=53.4070755022832x_{8} = 53.4070755022832
x9=−65.9734457648377x_{9} = -65.9734457648377
x10=−84.8230023359423x_{10} = -84.8230023359423
x11=59.6902606242892x_{11} = 59.6902606242892
x12=25.1327406025294x_{12} = 25.1327406025294
x13=−6.28318511636354x_{13} = -6.28318511636354
x14=15.7079634638398x_{14} = 15.7079634638398
x15=−18.8495552629365x_{15} = -18.8495552629365
x16=−78.5398159881807x_{16} = -78.5398159881807
x17=37.6991120440566x_{17} = 37.6991120440566
x18=−40.8407051595079x_{18} = -40.8407051595079
x19=−100.530964569618x_{19} = -100.530964569618
x20=−15.7079632966714x_{20} = -15.7079632966714
x21=−28.2743336965558x_{21} = -28.2743336965558
x22=−91.1061873420292x_{22} = -91.1061873420292
x23=−97.3893724672266x_{23} = -97.3893724672266
x24=75.3982240843678x_{24} = 75.3982240843678
x25=−12.5663702433638x_{25} = -12.5663702433638
x26=47.1238891892412x_{26} = 47.1238891892412
x27=21.9911485852154x_{27} = 21.9911485852154
x28=−31.4159267270698x_{28} = -31.4159267270698
x29=−87.9645943584581x_{29} = -87.9645943584581
x30=28.274333865158x_{30} = 28.274333865158
x31=100.530964752721x_{31} = 100.530964752721
x32=−69.1150387601409x_{32} = -69.1150387601409
x33=−9.42477814706151x_{33} = -9.42477814706151
x34=−94.2477794370922x_{34} = -94.2477794370922
x35=69.1150377756597x_{35} = 69.1150377756597
x36=91.1061876809771x_{36} = 91.1061876809771
x37=−72.2566308569174x_{37} = -72.2566308569174
x38=−43.9822971744994x_{38} = -43.9822971744994
x39=9.42477833842133x_{39} = 9.42477833842133
x40=72.2566310277163x_{40} = 72.2566310277163
x41=25.1327419134392x_{41} = 25.1327419134392
x42=−25.1327415966545x_{42} = -25.1327415966545
x43=91.1061863617978x_{43} = 91.1061863617978
x44=87.9645943360531x_{44} = 87.9645943360531
x45=65.9734457530652x_{45} = 65.9734457530652
x46=81.6814092045399x_{46} = 81.6814092045399
x47=97.3893726665604x_{47} = 97.3893726665604
x48=40.8407041479024x_{48} = 40.8407041479024
x49=−47.1238901783506x_{49} = -47.1238901783506
x50=−40.8407038505852x_{50} = -40.8407038505852
x51=−62.8318537475395x_{51} = -62.8318537475395
x52=34.5575190128984x_{52} = 34.5575190128984
x53=69.1150390913744x_{53} = 69.1150390913744
x54=47.1238905022021x_{54} = 47.1238905022021
x55=−53.4070753070989x_{55} = -53.4070753070989
x56=94.2477796093522x_{56} = 94.2477796093522
x57=−75.3982238871507x_{57} = -75.3982238871507
x58=−21.9911485864319x_{58} = -21.9911485864319
x59=56.5486675928533x_{59} = 56.5486675928533
x60=6.28318528416575x_{60} = 6.28318528416575
x61=−18.8495565718301x_{61} = -18.8495565718301
x62=3.14159201551055x_{62} = 3.14159201551055
x63=78.5398161727936x_{63} = 78.5398161727936
x64=62.8318527292552x_{64} = 62.8318527292552
x65=−81.6814090384499x_{65} = -81.6814090384499
x66=18.8495555664687x_{66} = 18.8495555664687
x67=31.4159269203024x_{67} = 31.4159269203024
x68=84.82300131053x_{68} = 84.82300131053
x69=−3.14159301504925x_{69} = -3.14159301504925
x70=−50.2654822767396x_{70} = -50.2654822767396
x71=−56.5486674066613x_{71} = -56.5486674066613
x72=−84.8230010248866x_{72} = -84.8230010248866
x73=0x_{73} = 0
x74=43.9822971695024x_{74} = 43.9822971695024
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 tan(x)*sin(x).
sin⁡(0)tan⁡(0)\sin{\left(0 \right)} \tan{\left(0 \right)}
Resultado:
f(0)=0f{\left(0 \right)} = 0
Punto:
(0, 0)
Asíntotas horizontales
Hallemos las asíntotas horizontales mediante los límites de esta función con x->+oo y x->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la izquierda:
y=lim⁡x→−∞(sin⁡(x)tan⁡(x))y = \lim_{x \to -\infty}\left(\sin{\left(x \right)} \tan{\left(x \right)}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota horizontal a la derecha:
y=lim⁡x→∞(sin⁡(x)tan⁡(x))y = \lim_{x \to \infty}\left(\sin{\left(x \right)} \tan{\left(x \right)}\right)
Asíntotas inclinadas
Se puede hallar la asíntota inclinada calculando el límite de la función tan(x)*sin(x), dividida por x con x->+oo y x ->-oo
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la izquierda:
y=xlim⁡x→−∞(sin⁡(x)tan⁡(x)x)y = x \lim_{x \to -\infty}\left(\frac{\sin{\left(x \right)} \tan{\left(x \right)}}{x}\right)
True

Tomamos como el límite
es decir,
ecuación de la asíntota inclinada a la derecha:
y=xlim⁡x→∞(sin⁡(x)tan⁡(x)x)y = x \lim_{x \to \infty}\left(\frac{\sin{\left(x \right)} \tan{\left(x \right)}}{x}\right)
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)tan⁡(x)=sin⁡(x)tan⁡(x)\sin{\left(x \right)} \tan{\left(x \right)} = \sin{\left(x \right)} \tan{\left(x \right)}
- No
sin⁡(x)tan⁡(x)=−sin⁡(x)tan⁡(x)\sin{\left(x \right)} \tan{\left(x \right)} = - \sin{\left(x \right)} \tan{\left(x \right)}
- No
es decir, función
no es
par ni impar
Gráfico
Gráfico de la función y = tan(x)*sin(x)
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