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tan(x/2)=0.567 equation

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Numerical solution:

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The solution

You have entered [src]
   /x\   567 
tan|-| = ----
   \2/   1000
$$\tan{\left(\frac{x}{2} \right)} = \frac{567}{1000}$$
Detail solution
Given the equation
$$\tan{\left(\frac{x}{2} \right)} = \frac{567}{1000}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
Or
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + 2 \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
The graph
Rapid solution [src]
           /567 \
x1 = 2*atan|----|
           \1000/
$$x_{1} = 2 \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
x1 = 2*atan(567/1000)
Sum and product of roots [src]
sum
      /567 \
2*atan|----|
      \1000/
$$2 \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
=
      /567 \
2*atan|----|
      \1000/
$$2 \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
product
      /567 \
2*atan|----|
      \1000/
$$2 \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
=
      /567 \
2*atan|----|
      \1000/
$$2 \operatorname{atan}{\left(\frac{567}{1000} \right)}$$
2*atan(567/1000)
Numerical answer [src]
x1 = -30.3843239673945
x2 = 13.5979731828626
x3 = 63.8634556402993
x4 = -55.5170651961128
x5 = -61.8002505032924
x6 = -80.6498064248312
x7 = -24.1011386602149
x8 = 7.31478787568305
x9 = 38.730714411581
x10 = -93.2161770391903
x11 = -17.8179533530353
x12 = -68.083435810472
x13 = 88.9961968690177
x14 = -86.9329917320107
x15 = -74.3666211176516
x16 = -5.25158273867613
x17 = 57.5802703331197
x18 = 95.2793821761973
x19 = -11.5347680458557
x20 = -49.2338798889332
x21 = -99.4993623463699
x22 = 26.1643437972218
x23 = -36.6675092745741
x24 = 70.1466409474789
x25 = 19.8811584900422
x26 = 45.0138997187606
x27 = 51.2970850259401
x28 = 82.7130115618381
x29 = 32.4475291044014
x30 = 1.03160256850346
x31 = 101.562567483377
x32 = -42.9506945817536
x33 = 76.4298262546585
x33 = 76.4298262546585