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sin(x)=1/sqrt(2) equation

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Numerical solution:

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The solution

You have entered [src]
             1  
sin(x) = 1*-----
             ___
           \/ 2 
$$\sin{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{2}}$$
Detail solution
Given the equation
$$\sin{\left(x \right)} = 1 \cdot \frac{1}{\sqrt{2}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{2}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{4}$$
$$x = 2 \pi n + \frac{3 \pi}{4}$$
, where n - is a integer
Rapid solution [src]
     pi
x1 = --
     4 
$$x_{1} = \frac{\pi}{4}$$
     3*pi
x2 = ----
      4  
$$x_{2} = \frac{3 \pi}{4}$$
Sum and product of roots [src]
sum
    pi   3*pi
0 + -- + ----
    4     4  
$$\left(0 + \frac{\pi}{4}\right) + \frac{3 \pi}{4}$$
=
pi
$$\pi$$
product
  pi 3*pi
1*--*----
  4   4  
$$\frac{3 \pi}{4} \cdot 1 \frac{\pi}{4}$$
=
    2
3*pi 
-----
  16 
$$\frac{3 \pi^{2}}{16}$$
3*pi^2/16
Numerical answer [src]
x1 = 84.037603483527
x2 = 46.3384916404494
x3 = -99.7455667514759
x4 = 128.019900633784
x5 = 0.785398163397448
x6 = 52.621676947629
x7 = 14.9225651045515
x8 = 6964.12551484517
x9 = 44.7676953136546
x10 = 57.3340659280137
x11 = -54.1924732744239
x12 = 7.06858347057703
x13 = 38.484510006475
x14 = -73.0420291959627
x15 = -24.3473430653209
x16 = -1160.03308733803
x17 = 40.0553063332699
x18 = -60.4756585816035
x19 = 25.9181393921158
x20 = 2476.36040919215
x21 = -17680.09805624
x22 = -49.4800842940392
x23 = 63.6172512351933
x24 = 2.35619449019234
x25 = -186.139364725195
x26 = -36.9137136796801
x27 = -22.776546738526
x28 = 2151.20556954561
x29 = -35.3429173528852
x30 = 21.2057504117311
x31 = 90.3207887907066
x32 = 71.4712328691678
x33 = -237.975643509427
x34 = -118.595122673015
x35 = -80.8960108299372
x36 = 33.7721210260903
x37 = 69.9004365423729
x38 = -47.9092879672443
x39 = -29.0597320457056
x40 = -41.6261026600648
x41 = -62.0464549083984
x42 = -66.7588438887831
x43 = 95.0331777710912
x44 = 32.2013246992954
x45 = -3.92699081698724
x46 = -79.3252145031423
x47 = 96.6039740978861
x48 = -74.6128255227576
x49 = -11.7809724509617
x50 = 76.1836218495525
x51 = 13.3517687777566
x52 = 8.63937979737193
x53 = 27.4889357189107
x54 = 77.7544181763474
x55 = -30.6305283725005
x56 = -85.6083998103219
x57 = -98.174770424681
x58 = -55.7632696012188
x59 = 19.6349540849362
x60 = -87.1791961371168
x61 = -16.4933614313464
x62 = 88.7499924639117
x63 = -68.329640215578
x64 = -43.1968989868597
x65 = -18.0641577581413
x66 = -10.2101761241668
x67 = 58.9048622548086
x68 = 51.0508806208341
x69 = -93.4623814442964
x70 = 65.1880475619882
x71 = -91.8915851175014
x72 = 82.4668071567321
x73 = 101.316363078271
x74 = -5.49778714378214
x74 = -5.49778714378214