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cos(x)x(cos(x)/2(sin(x)^3)^0.5) equation

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Numerical solution:

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The solution

You have entered [src] 
                   _________    
         cos(x)   /    3        
cos(x)*x*------*\/  sin (x)  = 0
           2
$$x \cos{\left(x \right)} \frac{\cos{\left(x \right)}}{2} \sqrt{\sin^{3}{\left(x \right)}} = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = 0
$$x_{1} = 0$$ 
     pi
x2 = --
     2
$$x_{2} = \frac{\pi}{2}$$ 
x3 = pi
$$x_{3} = \pi$$ 
     3*pi
x4 = ----
      2
$$x_{4} = \frac{3 \pi}{2}$$ 
x4 = 3*pi/2
Sum and product of roots [src] 
sum
pi        3*pi
-- + pi + ----
2          2
$$\left(\frac{\pi}{2} + \pi\right) + \frac{3 \pi}{2}$$ 
=
3*pi
$$3 \pi$$ 
product
  pi    3*pi
0*--*pi*----
  2      2
$$\frac{3 \pi}{2} \pi 0 \frac{\pi}{2}$$ 
=
0
$$0$$ 
0
Numerical answer [src] 
x1 = 86.3937978925496
x2 = 105.24335388818
x3 = -21.9911485751319 + 1.21701331436825e-12*i
x4 = -9.42477796077199
x5 = -6.28318530717858
x6 = -86.3937978454951
x7 = 21.991148575131
x8 = 65.9734457253915
x9 = 89.5353907193696
x10 = -45.5530935800067
x11 = -73.8274272808293
x12 = -42.4115007030314
x13 = 50.2654824574343
x14 = 59.6902604182087
x15 = 64.4026493137127
x16 = -43.9822971502648 - 1.00959350293142e-12*i
x17 = 87.9645943005214
x18 = 43.9822971502614
x19 = 100.530964914865
x20 = -37.6991118430841
x21 = 12.5663706143661 - 1.19923455056577e-12*i
x22 = 4.71238895210165
x23 = 72.2566310325642
x24 = -53.4070751109997 + 6.62989326283228e-12*i
x25 = -97.3893722612291 + 1.92562515522325e-11*i
x26 = -94.2477796076814
x27 = 87.9645943006641 + 4.72161898657479e-14*i
x28 = 3.14159265483036 + 6.53701670193335e-10*i
x29 = -67.5442421580059
x30 = 42.4115007351001
x31 = 92.676983166985
x32 = 95.818576047059
x33 = -95.8185758684718
x34 = 37.6991118430831
x35 = -14.1371668478262
x36 = -81.6814089933429
x37 = 34.557519189487
x38 = -64.4026492736812
x39 = 94.2477796076942 - 2.58917802018419e-14*i
x40 = -23.5619450021987
x41 = 0.0
x42 = 14.1371670880956
x43 = -58.1194640048268
x44 = -36.1283154258118
x45 = -75.3982236861367 - 5.00976358880785e-12*i
x46 = 20.420352157043
x47 = -31.4159265358915 - 1.00935292732798e-12*i
x48 = 81.681408993333 - 1.02778347670323e-13*i
x49 = -94.2477796083936 - 5.36697903487868e-11*i
x50 = -59.690260417908 + 1.05848716888913e-11*i
x51 = -50.2654824574264
x52 = 2.65355322545033e-6 + 4.97124619708737e-8*i
x53 = 26.7035374640549
x54 = 15.7079632679578
x55 = 51.8362788906682
x56 = 45.553093585641
x57 = -17.2787596900909
x58 = 7.85398173605402
x59 = 89.5353906206004
x60 = 70.6858345971581
x61 = -20.4203521358759
x62 = -7.85398150943291
x63 = 1.57079651739021
x64 = -65.9734457253944 + 6.75779611221377e-12*i
x65 = -61.2610568093874
x66 = 28.2743338823046
x67 = -89.5353907359556
x68 = -87.9645943005313 - 3.81553787022826e-12*i
x69 = -29.8451301000153
x70 = -51.8362786914272
x71 = 73.8274274689137
x72 = 29.8451303124659
x73 = -1.57079643713702
x74 = -59.6902604182135
x75 = 1.57079542412936 + 3.5960363001003e-7*i
x76 = 10.9955739674327 + 3.78558571416213e-14*i
x77 = -80.1106125841884
x78 = 56.5486677646122
x79 = -83.2522053690997
x80 = 6.28318530717511
x81 = -3.14159265430334 - 9.48283722326023e-12*i
x82 = 67.5442421528063
x83 = -72.2566310325538
x84 = -15.7079632679546
x85 = -39.2699082484219
x86 = -28.2743338822997
x87 = 78.5398163397385
x88 = 48.6946860288712
x89 = 23.5619450194929
x89 = 23.5619450194929
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