sin3x-1=0 (уравнение)

Найду корень уравнения: sin3x-1=0

Вы ввели

sin(3*x) - 1 = 0

$$\sin{\left(3 x \right)} - 1 = 0$$

Подробное решение

Дано уравнение
$$\sin{\left(3 x \right)} - 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$\sin{\left(3 x \right)} - 1 + 1 = 1$$
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 = -35.081117920222

x2 = 6.8067839497432

x3 = 86.3937978904858

x4 = 52.8834762893477

x5 = -64.4026492298162

x6 = -22.5147471967799

x7 = 42.411500732115

x8 = -93.7241808501502

x9 = 63.3554518703442

x10 = -81.1578103224548

x11 = 2.61799372149593

x12 = 88.4881929539175

x13 = 31.9395253654771

x14 = 21.4675499464553

x15 = -58.1194640021532

x16 = 23.5619450702353

x17 = -20.4203520794005

x18 = -87.4409956689738

x19 = -18.3259569854581

x20 = -91.6297858015358

x21 = 17.2787592807644

x22 = 29.845130315527

x23 = -41.3643034312689

x24 = -3.66519119284134

x25 = 44.5058957975625

x26 = -26.7035377567181

x27 = 48.6946859683928

x28 = -47.6474886422567

x29 = 50.789081090574

x30 = -49.7418836877459

x31 = -53.9306741017977

x32 = -60.2138590635982

x33 = -85.3466004035061

x34 = -62.308254139164

x35 = 65.4498470876666

x36 = -66.4970445282258

x37 = 82.2050078076434

x38 = -24.6091423681141

x39 = -1.57079642588424

x40 = 78.0162175420896

x41 = -37.1755131460154

x42 = -12.0427717978327

x43 = -16.2315619072654

x44 = -39.2699083292704

x45 = -66.4970443416682

x46 = -83.252205476317

x47 = 38.2227106406479

x48 = 10.9955746928717

x49 = 25.6563401677065

x50 = 4.71238881902407

x51 = -68.5914394976747

x52 = 98.9601688300381

x53 = -28.7979326032841

x54 = 0.523598641616331

x55 = -43.458698513903

x56 = 71.733032403968

x57 = 46.6002908748595

x58 = -7.85398150192478

x59 = 69.6386373203027

x60 = -89.5353907407704

x61 = -85.3466005833809

x62 = -14.1371668430111

x63 = 75.9218225274375

x64 = -45.5530935835137

x65 = 67.5442422190054

x66 = 34.0339203588006

x67 = -51.8362786904677

x68 = 61.2610563291673

x69 = 27.7507352485908

x70 = 54.977871797926

x71 = 84.2994028383437

x72 = -70.6858348165339

x73 = -9.94837684428868

x74 = -37.1755131881972

x75 = 96.865773409958

x76 = -3.66519148254904

x77 = 90.5825880287766

x78 = 19.3731547552869

x79 = -95.8185758682622

x80 = 8.90117917814493

x81 = -5.75958652427337

x82 = 80.1106131528868

x83 = -79.0634150011636

x84 = 94.7713782337162

x85 = 73.8274274735132

x86 = 40.31710567763

x87 = -100.007366130834

x88 = -56.0250689629876

x89 = 92.6769831186997

График