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3sinx-1=0 equation

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Numerical solution:

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The solution

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3*sin(x) - 1 = 0
3sin⁡(x)−1=03 \sin{\left(x \right)} - 1 = 0
Simplify
Detail solution
Given the equation
3sin⁡(x)−1=03 \sin{\left(x \right)} - 1 = 0
- this is the simplest trigonometric equation
Move -1 to right part of the equation

with the change of sign in -1

We get:
3sin⁡(x)=13 \sin{\left(x \right)} = 1
Divide both parts of the equation by 3

The equation is transformed to
sin⁡(x)=13\sin{\left(x \right)} = \frac{1}{3}
This equation is transformed to
x=2πn+asin⁡(13)x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}
x=2πn−asin⁡(13)+πx = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi
Or
x=2πn+asin⁡(13)x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{3} \right)}
x=2πn−asin⁡(13)+πx = 2 \pi n - \operatorname{asin}{\left(\frac{1}{3} \right)} + \pi
, where n - is a integer
The graph
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = pi - asin(1/3)
x1=π−asin⁡(13)x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{3} \right)} 
x2 = asin(1/3)
x2=asin⁡(13)x_{2} = \operatorname{asin}{\left(\frac{1}{3} \right)} 
x2 = asin(1/3)
Sum and product of roots [src] 
sum
pi - asin(1/3) + asin(1/3)
asin⁡(13)+(π−asin⁡(13))\operatorname{asin}{\left(\frac{1}{3} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{1}{3} \right)}\right) 
=
pi
π\pi 
product
(pi - asin(1/3))*asin(1/3)
(π−asin⁡(13))asin⁡(13)\left(\pi - \operatorname{asin}{\left(\frac{1}{3} \right)}\right) \operatorname{asin}{\left(\frac{1}{3} \right)} 
=
(pi - asin(1/3))*asin(1/3)
(π−asin⁡(13))asin⁡(13)\left(\pi - \operatorname{asin}{\left(\frac{1}{3} \right)}\right) \operatorname{asin}{\left(\frac{1}{3} \right)} 
(pi - asin(1/3))*asin(1/3)
Numerical answer [src] 
x1 = -41.1805414061214
x2 = 25.4725781381725
x3 = 21.6513116656744
x4 = -43.642460240803
x5 = 75.7380605956092
x6 = -100.191128005419
x7 = -34.8973560989418
x8 = 38.0389487525316
x9 = -18.5097190120846
x10 = 15.3681263584948
x11 = -56.2088308551622
x12 = 44.3221340597112
x13 = 40.5008675872132
x14 = 6.62302221663371
x15 = 59.350423508752
x16 = -72.5964679420194
x17 = 2.80175574413567
x18 = 46.7840528943928
x19 = -12.2265337049051
x20 = -16.0478001774031
x21 = 69.4548752884296
x22 = -53.7469120204806
x23 = -47.463726713301
x24 = 65.6336088159315
x25 = 94.5876165171479
x26 = 9.08494105131526
x27 = 34.2176822800336
x28 = -49.9256455479826
x29 = -66.3132826348398
x30 = 31.7557634453521
x31 = -85.1628385563785
x32 = -75.0583867767009
x33 = -68.7752014695213
x34 = 71.9167941231111
x35 = 97.0495353518295
x36 = -78.879653249199
x37 = 19.1893928309929
x38 = -37.3592749336234
x39 = 53.0672382015724
x40 = 63.17168998125
x41 = -116.578765092276
x42 = -28.6141707917623
x43 = -9.7646148702235
x44 = -62.4920161623417
x45 = -93.9079426982397
x46 = 12.9062075238133
x47 = 172.447759037984
x48 = 0.339836909454122
x49 = 88.3044312099683
x50 = 82.0212459027887
x51 = 90.7663500446499
x52 = 78.1999794302907
x53 = 84.4831647374703
x54 = -81.3415720838805
x55 = -91.4460238635581
x56 = 56.8885046740704
x57 = -31.0760896264438
x58 = 27.934496972854
x59 = -5.94334839772546
x60 = -60.0300973276602
x61 = -3.48142956304392
x62 = 100.870801824328
x63 = 50.6053193668908
x64 = -97.7292091707377
x65 = -87.6247573910601
x66 = -22.3309854845827
x67 = -24.7929043192642
x67 = -24.7929043192642
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