sin(3x)=1 (уравнение)

Найду корень уравнения: sin(3x)=1

Вы ввели

sin(3*x) = 1

$$\sin{\left(3 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\sin{\left(3 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$3 x = 2 \pi n + \operatorname{asin}{\left(1 \right)}$$
$$3 x = 2 \pi n - \operatorname{asin}{\left(1 \right)} + \pi$$
Или
$$3 x = 2 \pi n + \frac{\pi}{2}$$
$$3 x = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$3$$
получим ответ:
$$x_{1} = \frac{2 \pi n}{3} + \frac{\pi}{6}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{\pi}{6}$$

Быстрый ответ

     pi
x1 = --
     6 

$$x_{1} = \frac{\pi}{6}$$

Сумма и произведение корней

сумма

    pi
0 + --
    6 

$$0 + \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

произведение

  pi
1*--
  6 

$$1 \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

Численный ответ

x1 = 40.31710567763

x2 = 78.0162175420896

x3 = -62.308254139164

x4 = -16.2315619072654

x5 = 46.6002908748595

x6 = 34.0339203588006

x7 = -1.57079642588424

x8 = 75.9218225274375

x9 = 31.9395253654771

x10 = 86.3937978904858

x11 = -87.4409956689738

x12 = 17.2787592807644

x13 = 50.789081090574

x14 = -20.4203520794005

x15 = -60.2138590635982

x16 = -9.94837684428868

x17 = 54.977871797926

x18 = 8.90117917814493

x19 = 44.5058957975625

x20 = -85.3466004035061

x21 = 38.2227106406479

x22 = 73.8274274735132

x23 = 4.71238881902407

x24 = -70.6858348165339

x25 = 71.733032403968

x26 = 65.4498470876666

x27 = -79.0634150011636

x28 = 48.6946859683928

x29 = -81.1578103224548

x30 = 98.9601688300381

x31 = 84.2994028383437

x32 = -24.6091423681141

x33 = -22.5147471967799

x34 = -35.081117920222

x35 = 61.2610563291673

x36 = 92.6769831186997

x37 = -47.6474886422567

x38 = 27.7507352485908

x39 = 90.5825880287766

x40 = 25.6563401677065

x41 = -12.0427717978327

x42 = -51.8362786904677

x43 = -83.252205476317

x44 = -68.5914394976747

x45 = -53.9306741017977

x46 = -66.4970443416682

x47 = 21.4675499464553

x48 = 82.2050078076434

x49 = -95.8185758682622

x50 = -45.5530935835137

x51 = -66.4970445282258

x52 = -89.5353907407704

x53 = 42.411500732115

x54 = 19.3731547552869

x55 = -85.3466005833809

x56 = -93.7241808501502

x57 = -3.66519119284134

x58 = -26.7035377567181

x59 = -37.1755131460154

x60 = 29.845130315527

x61 = 80.1106131528868

x62 = -37.1755131881972

x63 = 0.523598641616331

x64 = -14.1371668430111

x65 = -3.66519148254904

x66 = -5.75958652427337

x67 = 96.865773409958

x68 = -100.007366130834

x69 = -28.7979326032841

x70 = 67.5442422190054

x71 = 94.7713782337162

x72 = -58.1194640021532

x73 = -43.458698513903

x74 = -7.85398150192478

x75 = 10.9955746928717

x76 = 23.5619450702353

x77 = -18.3259569854581

x78 = -41.3643034312689

x79 = 69.6386373203027

x80 = 2.61799372149593

x81 = 6.8067839497432

x82 = 52.8834762893477

x83 = -91.6297858015358

x84 = 63.3554518703442

x85 = 88.4881929539175

x86 = -49.7418836877459

x87 = -56.0250689629876

x88 = -64.4026492298162

x89 = -39.2699083292704

График