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  • Identical expressions

  • ninety-eight *sin(x)/ five
  • 98 multiply by sinus of (x) divide by 5
  • ninety minus eight multiply by sinus of (x) divide by five
  • 98sin(x)/5
  • 98sinx/5
  • 98*sin(x) divide by 5

  • Similar expressions

  • 98*sinx/5
Plotting a function graph/ 98*sin(x)/5

Graphing y = 98*sin(x)/5

v

The graph:

from to

Intersection points:

does show?

Piecewise:

The solution

You have entered [src] 
       98*sin(x)
f(x) = ---------
           5
f(x)=98sin⁡(x)5f{\left(x \right)} = \frac{98 \sin{\left(x \right)}}{5} 
f = (98*sin(x))/5
The graph of the function
02468-8-6-4-2-1010-5050
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:
98sin⁡(x)5=0\frac{98 \sin{\left(x \right)}}{5} = 0
Solve this equation
The points of intersection with the axis X:

Analytical solution
x1=0x_{1} = 0
x2=πx_{2} = \pi
Numerical solution
x1=40.8407044966673x_{1} = 40.8407044966673
x2=−267.035375555132x_{2} = -267.035375555132
x3=0x_{3} = 0
x4=−18.8495559215388x_{4} = -18.8495559215388
x5=−56.5486677646163x_{5} = -56.5486677646163
x6=97.3893722612836x_{6} = 97.3893722612836
x7=34.5575191894877x_{7} = 34.5575191894877
x8=53.4070751110265x_{8} = 53.4070751110265
x9=47.1238898038469x_{9} = 47.1238898038469
x10=−97.3893722612836x_{10} = -97.3893722612836
x11=62.8318530717959x_{11} = 62.8318530717959
x12=87.9645943005142x_{12} = 87.9645943005142
x13=43.9822971502571x_{13} = 43.9822971502571
x14=37.6991118430775x_{14} = 37.6991118430775
x15=−21.9911485751286x_{15} = -21.9911485751286
x16=3.14159265358979x_{16} = 3.14159265358979
x17=69.1150383789755x_{17} = 69.1150383789755
x18=65.9734457253857x_{18} = 65.9734457253857
x19=−50.2654824574367x_{19} = -50.2654824574367
x20=−94.2477796076938x_{20} = -94.2477796076938
x21=−75.398223686155x_{21} = -75.398223686155
x22=−53.4070751110265x_{22} = -53.4070751110265
x23=12.5663706143592x_{23} = 12.5663706143592
x24=−9.42477796076938x_{24} = -9.42477796076938
x25=−113.097335529233x_{25} = -113.097335529233
x26=−34.5575191894877x_{26} = -34.5575191894877
x27=21.9911485751286x_{27} = 21.9911485751286
x28=−47.1238898038469x_{28} = -47.1238898038469
x29=−43.9822971502571x_{29} = -43.9822971502571
x30=28.2743338823081x_{30} = 28.2743338823081
x31=−31.4159265358979x_{31} = -31.4159265358979
x32=−3.14159265358979x_{32} = -3.14159265358979
x33=−6.28318530717959x_{33} = -6.28318530717959
x34=−25.1327412287183x_{34} = -25.1327412287183
x35=−62.8318530717959x_{35} = -62.8318530717959
x36=31.4159265358979x_{36} = 31.4159265358979
x37=−65.9734457253857x_{37} = -65.9734457253857
x38=72.2566310325652x_{38} = 72.2566310325652
x39=−59.6902604182061x_{39} = -59.6902604182061
x40=94.2477796076938x_{40} = 94.2477796076938
x41=81.6814089933346x_{41} = 81.6814089933346
x42=−91.106186954104x_{42} = -91.106186954104
x43=−100.530964914873x_{43} = -100.530964914873
x44=59.6902604182061x_{44} = 59.6902604182061
x45=−40.8407044966673x_{45} = -40.8407044966673
x46=91.106186954104x_{46} = 91.106186954104
x47=78.5398163397448x_{47} = 78.5398163397448
x48=−12.5663706143592x_{48} = -12.5663706143592
x49=56.5486677646163x_{49} = 56.5486677646163
x50=84.8230016469244x_{50} = 84.8230016469244
x51=100.530964914873x_{51} = 100.530964914873
x52=−69.1150383789755x_{52} = -69.1150383789755
x53=9.42477796076938x_{53} = 9.42477796076938
x54=−84.8230016469244x_{54} = -84.8230016469244
x55=−78.5398163397448x_{55} = -78.5398163397448
x56=−87.9645943005142x_{56} = -87.9645943005142
x57=−81.6814089933346x_{57} = -81.6814089933346
x58=15.707963267949x_{58} = 15.707963267949
x59=−28.2743338823081x_{59} = -28.2743338823081
x60=−15.707963267949x_{60} = -15.707963267949
x61=−37.6991118430775x_{61} = -37.6991118430775
x62=18.8495559215388x_{62} = 18.8495559215388
x63=25.1327412287183x_{63} = 25.1327412287183
x64=50.2654824574367x_{64} = 50.2654824574367
x65=−72.2566310325652x_{65} = -72.2566310325652
x66=75.398223686155x_{66} = 75.398223686155
x67=−232.477856365645x_{67} = -232.477856365645
x68=6.28318530717959x_{68} = 6.28318530717959
The points of intersection with the Y axis coordinate
The graph crosses Y axis when x equals 0:
substitute x = 0 to (98*sin(x))/5.
98sin⁡(0)5\frac{98 \sin{\left(0 \right)}}{5}
The result:
f(0)=0f{\left(0 \right)} = 0
The point:
(0, 0)
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
98cos⁡(x)5=0\frac{98 \cos{\left(x \right)}}{5} = 0
Solve this equation
The roots of this equation
x1=π2x_{1} = \frac{\pi}{2}
x2=3π2x_{2} = \frac{3 \pi}{2}
The values of the extrema at the points:
 pi       
(--, 98/5)
 2        

 3*pi        
(----, -98/5)
  2


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:
Minima of the function at points:
x1=3π2x_{1} = \frac{3 \pi}{2}
Maxima of the function at points:
x1=π2x_{1} = \frac{\pi}{2}
Decreasing at intervals
(−∞,π2]∪[3π2,∞)\left(-\infty, \frac{\pi}{2}\right] \cup \left[\frac{3 \pi}{2}, \infty\right)
Increasing at intervals
[π2,3π2]\left[\frac{\pi}{2}, \frac{3 \pi}{2}\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
−98sin⁡(x)5=0- \frac{98 \sin{\left(x \right)}}{5} = 0
Solve this equation
The roots of this equation
x1=0x_{1} = 0
x2=πx_{2} = \pi

Сonvexity and concavity intervals:
Let’s find the intervals where the function is convex or concave, for this look at the behaviour of the function at the inflection points:
Concave at the intervals
(−∞,0]∪[π,∞)\left(-\infty, 0\right] \cup \left[\pi, \infty\right)
Convex at the intervals
[0,π]\left[0, \pi\right]
Horizontal asymptotes
Let’s find horizontal asymptotes with help of the limits of this function at x->+oo and x->-oo
lim⁡x→−∞(98sin⁡(x)5)=⟨−985,985⟩\lim_{x \to -\infty}\left(\frac{98 \sin{\left(x \right)}}{5}\right) = \left\langle - \frac{98}{5}, \frac{98}{5}\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the left:
y=⟨−985,985⟩y = \left\langle - \frac{98}{5}, \frac{98}{5}\right\rangle
lim⁡x→∞(98sin⁡(x)5)=⟨−985,985⟩\lim_{x \to \infty}\left(\frac{98 \sin{\left(x \right)}}{5}\right) = \left\langle - \frac{98}{5}, \frac{98}{5}\right\rangle
Let's take the limit
so,
equation of the horizontal asymptote on the right:
y=⟨−985,985⟩y = \left\langle - \frac{98}{5}, \frac{98}{5}\right\rangle
Inclined asymptotes
Inclined asymptote can be found by calculating the limit of (98*sin(x))/5, divided by x at x->+oo and x ->-oo
lim⁡x→−∞(98sin⁡(x)5x)=0\lim_{x \to -\infty}\left(\frac{98 \sin{\left(x \right)}}{5 x}\right) = 0
Let's take the limit
so,
inclined coincides with the horizontal asymptote on the right
lim⁡x→∞(98sin⁡(x)5x)=0\lim_{x \to \infty}\left(\frac{98 \sin{\left(x \right)}}{5 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:
98sin⁡(x)5=−98sin⁡(x)5\frac{98 \sin{\left(x \right)}}{5} = - \frac{98 \sin{\left(x \right)}}{5}
- No
98sin⁡(x)5=98sin⁡(x)5\frac{98 \sin{\left(x \right)}}{5} = \frac{98 \sin{\left(x \right)}}{5}
- No
so, the function
not is
neither even, nor odd
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