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  • Similar expressions

  • (sinx/4)^2-2*sinx/4*cosx/4+(cosx/4)^2=0
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(sinx/4)^2+2*sinx/4*cosx/4+(cosx/4)^2=0 equation

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Numerical solution:

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The solution

You have entered [src] 
            2*sin(x)                       
        2   --------*cos(x)           2    
/sin(x)\       4              /cos(x)\     
|------|  + --------------- + |------|  = 0
\  4   /           4          \  4   /
$$\left(\frac{\cos{\left(x \right)}}{4}\right)^{2} + \left(\left(\frac{\sin{\left(x \right)}}{4}\right)^{2} + \frac{\frac{2 \sin{\left(x \right)}}{4} \cos{\left(x \right)}}{4}\right) = 0$$
Simplify
The graph
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
     -pi 
x1 = ----
      4
$$x_{1} = - \frac{\pi}{4}$$ 
     3*pi
x2 = ----
      4
$$x_{2} = \frac{3 \pi}{4}$$ 
x2 = 3*pi/4
Sum and product of roots [src] 
sum
  pi   3*pi
- -- + ----
  4     4
$$- \frac{\pi}{4} + \frac{3 \pi}{4}$$ 
=
pi
--
2
$$\frac{\pi}{2}$$ 
product
-pi  3*pi
----*----
 4    4
$$- \frac{\pi}{4} \frac{3 \pi}{4}$$ 
=
     2
-3*pi 
------
  16
$$- \frac{3 \pi^{2}}{16}$$ 
-3*pi^2/16
Numerical answer [src] 
x1 = 30.6305281863893
x2 = 36.9137134309271
x3 = -35.3429178934093
x4 = -29.0597320982225
x5 = -98.1747703033985
x6 = 24.3473430043575
x7 = -51.0508806461775
x8 = -76.1836225361187
x9 = 40.0553062099627
x10 = 99.7455669089878
x11 = -16.4933611966261
x12 = 33.7721211721652
x13 = 5.49778738042301
x14 = -7.06858355298869
x15 = -57.3340661259123
x16 = -19.6349541554673
x17 = 49.4800845342934
x18 = 43.1968992294597
x19 = -47.9092893362492
x20 = -66.7588439932285
x21 = -3.92699107594367
x22 = -82.4668069282144
x23 = -10.2101759860574
x24 = 68.3296401645238
x25 = -79.3252147038408
x26 = 96.6039739773235
x27 = 58.9048620635881
x28 = 80.8960105951638
x29 = -95.033175211328
x30 = 93.462381687851
x31 = -7.0685837201977
x32 = -60.4756583509459
x33 = 18.0641575837788
x34 = 58.9048620066655
x35 = -63.6172513149926
x36 = 65.1880478021829
x37 = -60.4756585174615
x38 = 90.3207887447523
x39 = -44.7676954314418
x40 = 14.9225649892472
x41 = 71.471233111112
x42 = -0.785398304611266
x43 = -44.7676950635734
x44 = -95.0331777492301
x45 = 11.7809725930891
x46 = 36.9137135281996
x47 = 87.1791963746667
x48 = 21.2057506565108
x49 = 52.6216767646073
x50 = 96.6039739212089
x51 = -13.3517689698773
x52 = -66.758843637313
x53 = -41.6261027352652
x54 = -95.0331780209134
x55 = 55.7632697006301
x56 = 55.7632697511726
x57 = -38.4845097737495
x58 = -22.7765468685351
x59 = -0.785397916651749
x60 = 2.35619442440536
x61 = -101.316363786262
x62 = 43.1968988259316
x63 = -29.0597322955756
x64 = -35.3429175479242
x65 = 62.0464548195549
x66 = 8.63937960822746
x67 = 74.6128253428807
x68 = -85.608399894653
x69 = 80.896010582516
x70 = 46.3384915843947
x71 = 14.9225648553046
x72 = -88.7499922112266
x73 = -73.0420294459387
x74 = -91.8915845717239
x75 = -22.7765464900166
x76 = 87.1791959595656
x77 = 77.7544183301131
x78 = -54.1924731445711
x79 = -96953.4762786628
x80 = -88.7499925537801
x81 = -76.1836217239439
x82 = 27.4889359573966
x83 = -73.0420291965934
x84 = -38.4845103583538
x85 = 84.0376034199549
x86 = 62.0464547256144
x87 = -51.0508808708243
x88 = 65.1880473923958
x89 = -32.2013245652766
x90 = 21.2057502602382
x90 = 21.2057502602382
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