sin(4x)=1 (уравнение)

Найду корень уравнения: sin(4x)=1

Вы ввели

sin(4*x) = 1

$$\sin{\left(4 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(4 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$4 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$4 x = 2 \pi n + \frac{\pi}{2}$$
$$4 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$x_{2} = \frac{\pi n}{2} + \frac{\pi}{8}$$

Быстрый ответ

     pi
x1 = --
     8 

$$x_{1} = \frac{\pi}{8}$$

Сумма и произведение корней

сумма

    pi
0 + --
    8 

$$0 + \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

произведение

  pi
1*--
  8 

$$1 \frac{\pi}{8}$$

=

pi
--
8 

$$\frac{\pi}{8}$$

Численный ответ

x1 = 23.9546440259598

x2 = -15.3152642379275

x3 = 9.81747676783862

x4 = -81.2887099089205

x5 = -73.4347283951574

x6 = 97.782071459868

x7 = 72.6493300240099

x8 = -29.4524312449951

x9 = 22.3838475810827

x10 = 69.5077373387294

x11 = 96.2112750487236

x12 = 9.81747715075509

x13 = -42.018801721698

x14 = 83.6449045156666

x15 = -228.943564806969

x16 = 80.5033116353485

x17 = -87.5718953117726

x18 = -12.1736714270123

x19 = 45.9457926074387

x20 = -86.00109889071

x21 = -67.1515431778245

x22 = -48.3019869255039

x23 = -84.430302507019

x24 = -78.1471171614871

x25 = 67.9369411885029

x26 = 0.392699002218603

x27 = 162.184720622203

x28 = -64.009950305697

x29 = -42.0188021311225

x30 = 17.6714587968444

x31 = 89.9280897692015

x32 = -57.7267650260013

x33 = 53.7997743057058

x34 = 75.7909228828866

x35 = 25.525440266285

x36 = -62.4391539454797

x37 = -93.8550803968028

x38 = -34.1648200049742

x39 = -43.5895981550743

x40 = -35.7356164448818

x41 = -20.0276531385131

x42 = -100.138265740044

x43 = 66.3661447392409

x44 = 39.6626073702294

x45 = 30.2378293001575

x46 = -87.5718952244412

x47 = -21.598449576501

x48 = -59.2975613554301

x49 = 52.2289778825359

x50 = -65.5807467334992

x51 = 72.6493300141926

x52 = 74.2201264653626

x53 = -12.1736719262543

x54 = -95.4258769697172

x55 = 6.67588432482476

x56 = -71.8639318172356

x57 = -79.7179136068893

x58 = 44.3749961600903

x59 = 58.5121630587909

x60 = 94.6404785931085

x61 = 1.96349544400331

x62 = -92.2842840752935

x63 = -37.3064127981981

x64 = -7.46128266944874

x65 = -26.3108383510529

x66 = 14.5298659063767

x67 = -56.1559685831317

x68 = 3.53429172010594

x69 = 8.24668071816113

x70 = 25.5254403437163

x71 = 47.5165888062105

x72 = -4.31968977692752

x73 = -13.7444678635051

x74 = 82.0741078307881

x75 = 52.2289777791699

x76 = 28.6670328896188

x77 = -51.4435798202399

x78 = 50.6581814561062

x79 = 36.5210144824622

x80 = 31.808625728328

x81 = 88.3572933185348

x82 = -18.4568568311997

x83 = 91.4988858631041

x84 = -70.2931355002572

x85 = 61.6537559431866

x86 = -40.4480053866604

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