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  • How to use it?

  • Graphing y =:
  • -x^2-2x+15
  • ((x-1)/(x+1))^3
  • (x-1)^2*(x+2)
  • 2x^3+3x^2-1

  • Identical expressions

  • tan(tan(x))/sin(sin(x))
  • tangent of ( tangent of (x)) divide by sinus of ( sinus of (x))
  • tantanx/sinsinx
  • tan(tan(x)) divide by sin(sin(x))

  • Similar expressions

  • tan(tan(x))/sin(sinx)
Plotting a function graph/ tan(tan(x))/sin(sin(x))

Graphing y = tan(tan(x))/sin(sin(x))

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       tan(tan(x))
f(x) = -----------
       sin(sin(x))
f(x)=tan⁡(tan⁡(x))sin⁡(sin⁡(x))f{\left(x \right)} = \frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}} 
f = tan(tan(x))/sin(sin(x))
The graph of the function
02468-8-6-4-2-1010-10001000
The domain of the function
The points at which the function is not precisely defined:
x1=0x_{1} = 0
x2=3.14159265358979x_{2} = 3.14159265358979
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⁡(tan⁡(x))sin⁡(sin⁡(x))=0\frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}} = 0
Solve this equation
The points of intersection with the axis X:

Numerical solution
x1=92.3688142097829x_{1} = 92.3688142097829
x2=−89.8435596984251x_{2} = -89.8435596984251
x3=246.923192377915x_{3} = 246.923192377915
x4=−86.0856289026033x_{4} = -86.0856289026033
x5=158.571018876118x_{5} = 158.571018876118
x6=73.669596169072x_{6} = 73.669596169072
x7=8.16215070509047x_{7} = 8.16215070509047
x8=−83.5603743912455x_{8} = -83.5603743912455
x9=−64.0944803274748x_{9} = -64.0944803274748
x10=−95.9242837308692x_{10} = -95.9242837308692
x11=79.9527814762516x_{11} = 79.9527814762516
x12=−17.5869286658598x_{12} = -17.5869286658598
x13=−57.8112950202952x_{13} = -57.8112950202952
x14=51.7727026025533x_{14} = 51.7727026025533
x15=−70.5280035154822x_{15} = -70.5280035154822
x16=23.2537758308075x_{16} = 23.2537758308075
x17=−20.1121831772177x_{17} = -20.1121831772177
x18=−1.87896539791088x_{18} = -1.87896539791088
x19=−315.421892614658x_{19} = -315.421892614658
x20=−42.7196698945782x_{20} = -42.7196698945782
x21=20.4004605044607x_{21} = 20.4004605044607
x22=−95.5104068633727x_{22} = -95.5104068633727
x23=111.218370131322x_{23} = 111.218370131322
x24=42.253669633174x_{24} = 42.253669633174
x25=−35.8201464451666x_{25} = -35.8201464451666
x26=−95.5104068633728x_{26} = -95.5104068633728
x27=−10.8377430972761x_{27} = -10.8377430972761
x28=14.4453360122701x_{28} = 14.4453360122701
x29=−92.5191520906107x_{29} = -92.5191520906107
x30=−30.0029613993912x_{30} = -30.0029613993912
x31=−42.3584988627726x_{31} = -42.3584988627726
x32=−48.85251732093x_{32} = -48.85251732093
x33=−7.748273837594x_{33} = -7.748273837594
x34=48.3865170595258x_{34} = 48.3865170595258
x35=−42.1033317523462x_{35} = -42.1033317523462
x36=−900.374464324592x_{36} = -900.374464324592
x37=95.7549997528104x_{37} = 95.7549997528104
x38=96.1267450056047x_{38} = 96.1267450056047
x39=−70.9940037768863x_{39} = -70.9940037768863
x40=1.87896539791088x_{40} = 1.87896539791088
x41=−39.5780772409884x_{41} = -39.5780772409884
x42=−13.8289978700381x_{42} = -13.8289978700381
x43=−79.8024435954237x_{43} = -79.8024435954237
x44=−73.9852585496483x_{44} = -73.9852585496483
x45=51.9419865806121x_{45} = 51.9419865806121
x46=64.2448182083026x_{46} = 64.2448182083026
x47=10.6874052164483x_{47} = 10.6874052164483
x48=−74.1355964304761x_{48} = -74.1355964304761
x49=61.1032255547128x_{49} = 61.1032255547128
x50=54.6697023667054x_{50} = 54.6697023667054
x51=80.4187817376557x_{51} = 80.4187817376557
x52=−23.6676526983039x_{52} = -23.6676526983039
x53=−140.109042155862x_{53} = -140.109042155862
x54=57.8112950202952x_{54} = 57.8112950202952
x55=86.0856289026033x_{55} = 86.0856289026033
x56=58.4276331625272x_{56} = 58.4276331625272
x57=102.409930312784x_{57} = 102.409930312784
x58=83.146497523749x_{58} = 83.146497523749
x59=36.2861467065708x_{59} = 36.2861467065708
x60=−51.5281097131156x_{60} = -51.5281097131156
x61=4.40421990926871x_{61} = 4.40421990926871
x62=23.6676526983039x_{62} = 23.6676526983039
x63=35.8201464451666x_{63} = 35.8201464451666
x64=−60.952887673885x_{64} = -60.952887673885
x65=26.3953684843973x_{65} = 26.3953684843973
x66=70.3776656346544x_{66} = 70.3776656346544
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to tan(tan(x))/sin(sin(x)).
tan⁡(tan⁡(0))sin⁡(sin⁡(0))\frac{\tan{\left(\tan{\left(0 \right)} \right)}}{\sin{\left(\sin{\left(0 \right)} \right)}}
The result:
f(0)=NaNf{\left(0 \right)} = \text{NaN}
- the solutions of the equation d'not exist
Vertical asymptotes
Have:
x1=0x_{1} = 0
x2=3.14159265358979x_{2} = 3.14159265358979
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⁡(tan⁡(x))sin⁡(sin⁡(x)))y = \lim_{x \to -\infty}\left(\frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}}\right)
True

Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=lim⁡x→∞(tan⁡(tan⁡(x))sin⁡(sin⁡(x)))y = \lim_{x \to \infty}\left(\frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}}\right)
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of tan(tan(x))/sin(sin(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⁡(tan⁡(x))xsin⁡(sin⁡(x)))y = x \lim_{x \to -\infty}\left(\frac{\tan{\left(\tan{\left(x \right)} \right)}}{x \sin{\left(\sin{\left(x \right)} \right)}}\right)
True

Let's take the limit
so,
inclined asymptote equation on the right:
y=xlim⁡x→∞(tan⁡(tan⁡(x))xsin⁡(sin⁡(x)))y = x \lim_{x \to \infty}\left(\frac{\tan{\left(\tan{\left(x \right)} \right)}}{x \sin{\left(\sin{\left(x \right)} \right)}}\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⁡(tan⁡(x))sin⁡(sin⁡(x))=tan⁡(tan⁡(x))sin⁡(sin⁡(x))\frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}} = \frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}}
- No
tan⁡(tan⁡(x))sin⁡(sin⁡(x))=−tan⁡(tan⁡(x))sin⁡(sin⁡(x))\frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}} = - \frac{\tan{\left(\tan{\left(x \right)} \right)}}{\sin{\left(\sin{\left(x \right)} \right)}}
- No
so, the function
not is
neither even, nor odd
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